Newton's First Law of Motion - Revision history

Hnhan3: /* Simple */

2025-12-03T03:58:42Z

Simple

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	===Simple===		===Simple===

	Question 1: Suppose you want to push a box across a table in a straight line at a constant speed. What force, if any, would you have to exert on the box? (Describe it qualitatively- not enough information is supplied for a numerical answer.)		<i>Question 1:</i> Suppose you want to push a box across a table in a straight line at a constant speed. What force, if any, would you have to exert on the box? (Describe it qualitatively- not enough information is supplied for a numerical answer.)

	Answer: The moving box would experience 3 forces (besides any you exert on it): gravity, normal force from the table, and friction with the table and air. Gravity points downwards, normal force points upwards, and friction opposes the direction of motion. Because of the nature of normal force, the normal force takes on whatever magnitude necessary to cancel gravity. The only unbalanced force is therefore friction. Since your objective is to keep the box moving in a straight line at a constant speed (that is, at a constant velocity), the net force acting on the box must be 0 according to Newton's first law. The force you exert should therefore balance the friction force by being equal in magnitude and opposite in direction.		Answer: The moving box would experience 3 forces (besides any you exert on it): gravity, normal force from the table, and friction with the table and air. Gravity points downwards, normal force points upwards, and friction opposes the direction of motion. Because of the nature of normal force, the normal force takes on whatever magnitude necessary to cancel gravity. The only unbalanced force is therefore friction. Since your objective is to keep the box moving in a straight line at a constant speed (that is, at a constant velocity), the net force acting on the box must be 0 according to Newton's first law. The force you exert should therefore balance the friction force by being equal in magnitude and opposite in direction.

	Question 2: Is a change in position an indicator of interaction?		<i>Question 2:</i> Is a change in position an indicator of interaction?

	Answer: On its own, a change in position is not enough to indicate an interaction because an object can have a nonzero velocity (that is, have a changing position) even with no forces acting on it, so long as that velocity is constant. With some additional information, however, a change in position can indicate an interaction. For example, if an object is initially at rest and is later found at another position, its velocity must have changed and it must have been acted on by a nonzero unbalanced external force.		Answer: On its own, a change in position is not enough to indicate an interaction because an object can have a nonzero velocity (that is, have a changing position) even with no forces acting on it, so long as that velocity is constant. With some additional information, however, a change in position can indicate an interaction. For example, if an object is initially at rest and is later found at another position, its velocity must have changed and it must have been acted on by a nonzero unbalanced external force.

Hnhan3: /* Medium */

2025-12-03T03:58:02Z

Medium

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	===Medium===		===Medium===

	Question: A 16kg traffic light is suspended by two cables, each 22<math>^\circ</math> from horizontal, as shown below:		<i>Question:</i> A 16kg traffic light is suspended by two cables, each 22<math>^\circ</math> from horizontal, as shown below:

	[[File:Newtonsfirsttrafficlight.png]]		[[File:Newtonsfirsttrafficlight.png]]
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	What is the tension in each of the cables?		What is the tension in each of the cables?

	Solution: Because the traffic light is at rest and not accelerating, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the traffic light are gravity and tension in the 2 cables. The horizontal components of the cables' tension forces must be equal in magnitude, or the traffic light would be accelerating to the left or the right. Combining that information with the fact that the two cables are inclined by the same amount leads to the conclusion that the tension in the two cables must be the same. Finally, we know that the combined vertical components of the two cables' tension forces must equal the traffic light's weight, or the light would be accelerating vertically. This allows us to create the following equation:		<i>Solution:</i> Because the traffic light is at rest and not accelerating, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the traffic light are gravity and tension in the 2 cables. The horizontal components of the cables' tension forces must be equal in magnitude, or the traffic light would be accelerating to the left or the right. Combining that information with the fact that the two cables are inclined by the same amount leads to the conclusion that the tension in the two cables must be the same. Finally, we know that the combined vertical components of the two cables' tension forces must equal the traffic light's weight, or the light would be accelerating vertically. This allows us to create the following equation:

	<math>2T\sin(22) = 16*9.8</math>		<math>2T\sin(22) = 16*9.8</math>

Hnhan3: /* Difficult */

2025-12-03T03:57:38Z

Difficult

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	<i>Question:</i> Suppose there exists a car of mass 9000 kg that is moving at a constant speed of 90 m/s in an easterly direction. The car is being buffeted by a strong wind, which exerts a 1000N force on it in the northerly direction. From this information, you know that the coefficient of static friction between the road and teh car's tires <math>\mu_s</math> must be at least what value?		<i>Question:</i> Suppose there exists a car of mass 9000 kg that is moving at a constant speed of 90 m/s in an easterly direction. The car is being buffeted by a strong wind, which exerts a 1000N force on it in the northerly direction. From this information, you know that the coefficient of static friction between the road and teh car's tires <math>\mu_s</math> must be at least what value?

	<b>Solution:</b> Because the car is travelling at a constant speed without changing direction, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the car are gravity, the normal force from the road, the wind, and static friction with the road. Gravity acts in the downward direction, the normal force acts in the upward direction, the wind acts in a northerly direction, and static friction acts in a southerly direction. We know that the magnitude of the normal force must be equal to the magnitude of the gravitational force, or the car would be accelerating vertically. That is, the magnitude of the normal force <math>N</math> must be 9,000kg * 9.8m/s = 88200N. We also know that the magnitude of the static friction force must be equal to the magnitude of the wind force, or the car would be accelerating along the north-south axis. That is, the magnitude of the friction force <math>f_s</math> must be 1000N.		<i>Solution:</i> Because the car is travelling at a constant speed without changing direction, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the car are gravity, the normal force from the road, the wind, and static friction with the road. Gravity acts in the downward direction, the normal force acts in the upward direction, the wind acts in a northerly direction, and static friction acts in a southerly direction. We know that the magnitude of the normal force must be equal to the magnitude of the gravitational force, or the car would be accelerating vertically. That is, the magnitude of the normal force <math>N</math> must be 9,000kg * 9.8m/s = 88200N. We also know that the magnitude of the static friction force must be equal to the magnitude of the wind force, or the car would be accelerating along the north-south axis. That is, the magnitude of the friction force <math>f_s</math> must be 1000N.

	<math>f_s \leq \mu_s * N</math>		<math>f_s \leq \mu_s * N</math>

Hnhan3: /* Difficult */

2025-12-03T03:57:25Z

Difficult

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	(Requires knowledge of [[Static Friction]].)		(Requires knowledge of [[Static Friction]].)

	<b>Question:</b> Suppose there exists a car of mass 9000 kg that is moving at a constant speed of 90 m/s in an easterly direction. The car is being buffeted by a strong wind, which exerts a 1000N force on it in the northerly direction. From this information, you know that the coefficient of static friction between the road and teh car's tires <math>\mu_s</math> must be at least what value?		<i>Question:</i> Suppose there exists a car of mass 9000 kg that is moving at a constant speed of 90 m/s in an easterly direction. The car is being buffeted by a strong wind, which exerts a 1000N force on it in the northerly direction. From this information, you know that the coefficient of static friction between the road and teh car's tires <math>\mu_s</math> must be at least what value?

	<b>Solution:</b> Because the car is travelling at a constant speed without changing direction, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the car are gravity, the normal force from the road, the wind, and static friction with the road. Gravity acts in the downward direction, the normal force acts in the upward direction, the wind acts in a northerly direction, and static friction acts in a southerly direction. We know that the magnitude of the normal force must be equal to the magnitude of the gravitational force, or the car would be accelerating vertically. That is, the magnitude of the normal force <math>N</math> must be 9,000kg * 9.8m/s = 88200N. We also know that the magnitude of the static friction force must be equal to the magnitude of the wind force, or the car would be accelerating along the north-south axis. That is, the magnitude of the friction force <math>f_s</math> must be 1000N.		<b>Solution:</b> Because the car is travelling at a constant speed without changing direction, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the car are gravity, the normal force from the road, the wind, and static friction with the road. Gravity acts in the downward direction, the normal force acts in the upward direction, the wind acts in a northerly direction, and static friction acts in a southerly direction. We know that the magnitude of the normal force must be equal to the magnitude of the gravitational force, or the car would be accelerating vertically. That is, the magnitude of the normal force <math>N</math> must be 9,000kg * 9.8m/s = 88200N. We also know that the magnitude of the static friction force must be equal to the magnitude of the wind force, or the car would be accelerating along the north-south axis. That is, the magnitude of the friction force <math>f_s</math> must be 1000N.

Hnhan3: /* Difficult */

2025-12-03T03:57:12Z

Difficult

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	(Requires knowledge of [[Static Friction]].)		(Requires knowledge of [[Static Friction]].)

	Question: Suppose there exists a car of mass 9000 kg that is moving at a constant speed of 90 m/s in an easterly direction. The car is being buffeted by a strong wind, which exerts a 1000N force on it in the northerly direction. From this information, you know that the coefficient of static friction between the road and teh car's tires <math>\mu_s</math> must be at least what value?		<b>Question:</b> Suppose there exists a car of mass 9000 kg that is moving at a constant speed of 90 m/s in an easterly direction. The car is being buffeted by a strong wind, which exerts a 1000N force on it in the northerly direction. From this information, you know that the coefficient of static friction between the road and teh car's tires <math>\mu_s</math> must be at least what value?

	Solution: Because the car is travelling at a constant speed without changing direction, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the car are gravity, the normal force from the road, the wind, and static friction with the road. Gravity acts in the downward direction, the normal force acts in the upward direction, the wind acts in a northerly direction, and static friction acts in a southerly direction. We know that the magnitude of the normal force must be equal to the magnitude of the gravitational force, or the car would be accelerating vertically. That is, the magnitude of the normal force <math>N</math> must be 9,000kg * 9.8m/s = 88200N. We also know that the magnitude of the static friction force must be equal to the magnitude of the wind force, or the car would be accelerating along the north-south axis. That is, the magnitude of the friction force <math>f_s</math> must be 1000N.		<b>Solution:</b> Because the car is travelling at a constant speed without changing direction, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the car are gravity, the normal force from the road, the wind, and static friction with the road. Gravity acts in the downward direction, the normal force acts in the upward direction, the wind acts in a northerly direction, and static friction acts in a southerly direction. We know that the magnitude of the normal force must be equal to the magnitude of the gravitational force, or the car would be accelerating vertically. That is, the magnitude of the normal force <math>N</math> must be 9,000kg * 9.8m/s = 88200N. We also know that the magnitude of the static friction force must be equal to the magnitude of the wind force, or the car would be accelerating along the north-south axis. That is, the magnitude of the friction force <math>f_s</math> must be 1000N.

	<math>f_s \leq \mu_s * N</math>		<math>f_s \leq \mu_s * N</math>

Hnhan3: /* History */

2025-12-03T03:56:10Z

History

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	==History==		==History==

	The nature of the tendencies of matter regarding motion has been the subject of much thought throughout human history. Aristotle (384–322 BCE) famously believed that all objects have a "natural place" towards which they tend: heavy objects belong on the earth and therefore tend to move downwards, while lighter substances such as smoke belong in the sky and therefore tend to move upwards. Once an object reached its natural place, Aristotle believed, it would remain there at rest. Aristotle believed objects could not continue to move forever without being acted on by a force to keep it in motion, which is consistent with any observations he could have made on the surface of the earth, although today, we know this to be the result of [[Friction]].		The nature of the tendencies of matter regarding motion has been the subject of much thought throughout human history. <b>Aristotle (384–322 BCE)</b> famously believed that all objects have a "natural place" towards which they tend: heavy objects belong on the earth and therefore tend to move downwards, while lighter substances such as smoke belong in the sky and therefore tend to move upwards. Once an object reached its natural place, Aristotle believed, it would remain there at rest. Aristotle believed objects could not continue to move forever without being acted on by a force to keep it in motion, which is consistent with any observations he could have made on the surface of the earth, although today, we know this to be the result of [[Friction]].

	<b>Galileo Galilei (1564-1642)</b>, who studied the motion of celestial bodies, was the first to propose that perpetual motion was actually the natural state of objects, and that forces such as friction were necessary to bring them to rest or otherwise change their velocities. Galileo performed an experiment with two ramps and a bronze ball. The two ramps were set up at the same angle of incline, facing each other. Galileo observed that if a ball was released on one of the ramps from a certain height, it would roll down that ramp and up the other and reach that same height. He then experimented with altering the angle of the second ramp. He observed that even when the second ramp was less steep than the first, the ball would reach the same height it was dropped from. (Today, this is known to be the result of conservation of energy.) Galileo reasoned that if the second ramp were removed entirely, and the ball rolled down the first ramp and onto a flat surface, it would never be able to reach the height it was dropped from, and would therefore never stop moving if conditions were ideal. Galileo was essentially the first person to propose the idea that we now know as Newton's first law.		<b>Galileo Galilei (1564-1642)</b>, who studied the motion of celestial bodies, was the first to propose that perpetual motion was actually the natural state of objects, and that forces such as friction were necessary to bring them to rest or otherwise change their velocities. Galileo performed an experiment with two ramps and a bronze ball. The two ramps were set up at the same angle of incline, facing each other. Galileo observed that if a ball was released on one of the ramps from a certain height, it would roll down that ramp and up the other and reach that same height. He then experimented with altering the angle of the second ramp. He observed that even when the second ramp was less steep than the first, the ball would reach the same height it was dropped from. (Today, this is known to be the result of conservation of energy.) Galileo reasoned that if the second ramp were removed entirely, and the ball rolled down the first ramp and onto a flat surface, it would never be able to reach the height it was dropped from, and would therefore never stop moving if conditions were ideal. Galileo was essentially the first person to propose the idea that we now know as Newton's first law.

Hnhan3: /* History */

2025-12-03T03:55:30Z

History

← Older revision		Revision as of 23:55, 2 December 2025
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	<b>Galileo Galilei (1564-1642)</b>, who studied the motion of celestial bodies, was the first to propose that perpetual motion was actually the natural state of objects, and that forces such as friction were necessary to bring them to rest or otherwise change their velocities. Galileo performed an experiment with two ramps and a bronze ball. The two ramps were set up at the same angle of incline, facing each other. Galileo observed that if a ball was released on one of the ramps from a certain height, it would roll down that ramp and up the other and reach that same height. He then experimented with altering the angle of the second ramp. He observed that even when the second ramp was less steep than the first, the ball would reach the same height it was dropped from. (Today, this is known to be the result of conservation of energy.) Galileo reasoned that if the second ramp were removed entirely, and the ball rolled down the first ramp and onto a flat surface, it would never be able to reach the height it was dropped from, and would therefore never stop moving if conditions were ideal. Galileo was essentially the first person to propose the idea that we now know as Newton's first law.		<b>Galileo Galilei (1564-1642)</b>, who studied the motion of celestial bodies, was the first to propose that perpetual motion was actually the natural state of objects, and that forces such as friction were necessary to bring them to rest or otherwise change their velocities. Galileo performed an experiment with two ramps and a bronze ball. The two ramps were set up at the same angle of incline, facing each other. Galileo observed that if a ball was released on one of the ramps from a certain height, it would roll down that ramp and up the other and reach that same height. He then experimented with altering the angle of the second ramp. He observed that even when the second ramp was less steep than the first, the ball would reach the same height it was dropped from. (Today, this is known to be the result of conservation of energy.) Galileo reasoned that if the second ramp were removed entirely, and the ball rolled down the first ramp and onto a flat surface, it would never be able to reach the height it was dropped from, and would therefore never stop moving if conditions were ideal. Galileo was essentially the first person to propose the idea that we now know as Newton's first law.

	Isaac Newton (1643-1727) confirmed Galileo's idea with his own experiments and published it along with his 2 other laws in his 1687 work <i>Principia Mathematica</i>. Newton refined Galileo's concept by expanding it to add that objects at rest will stay at rest, unless acted upon by a force. Although he gave credit to Galileo, today the law is known by Newton's name.		<b>Isaac Newton (1643-1727)</b> confirmed Galileo's idea with his own experiments and published it along with his 2 other laws in his 1687 work <i>Principia Mathematica</i>. Newton refined Galileo's concept by expanding it to add that objects at rest will stay at rest, unless acted upon by a force. Although he gave credit to Galileo, today the law is known by Newton's name.

	Newton's first law appears in <i>Principia</i> (which was written in Latin) as follows:		Newton's first law appears in <i>Principia</i> (which was written in Latin) as follows:
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	Translated to English, this reads:		Translated to English, this reads:

	"Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed."		<b>"Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed."</b>

	Newton continued experimenting and found many fundamental ideas used in modern Physics today.		Newton continued experimenting and found many fundamental ideas used in modern Physics today.

Hnhan3: /* History */

2025-12-03T03:55:02Z

History

← Older revision		Revision as of 23:55, 2 December 2025
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	The nature of the tendencies of matter regarding motion has been the subject of much thought throughout human history. Aristotle (384–322 BCE) famously believed that all objects have a "natural place" towards which they tend: heavy objects belong on the earth and therefore tend to move downwards, while lighter substances such as smoke belong in the sky and therefore tend to move upwards. Once an object reached its natural place, Aristotle believed, it would remain there at rest. Aristotle believed objects could not continue to move forever without being acted on by a force to keep it in motion, which is consistent with any observations he could have made on the surface of the earth, although today, we know this to be the result of [[Friction]].		The nature of the tendencies of matter regarding motion has been the subject of much thought throughout human history. Aristotle (384–322 BCE) famously believed that all objects have a "natural place" towards which they tend: heavy objects belong on the earth and therefore tend to move downwards, while lighter substances such as smoke belong in the sky and therefore tend to move upwards. Once an object reached its natural place, Aristotle believed, it would remain there at rest. Aristotle believed objects could not continue to move forever without being acted on by a force to keep it in motion, which is consistent with any observations he could have made on the surface of the earth, although today, we know this to be the result of [[Friction]].

	Galileo Galilei (1564-1642), who studied the motion of celestial bodies, was the first to propose that perpetual motion was actually the natural state of objects, and that forces such as friction were necessary to bring them to rest or otherwise change their velocities. Galileo performed an experiment with two ramps and a bronze ball. The two ramps were set up at the same angle of incline, facing each other. Galileo observed that if a ball was released on one of the ramps from a certain height, it would roll down that ramp and up the other and reach that same height. He then experimented with altering the angle of the second ramp. He observed that even when the second ramp was less steep than the first, the ball would reach the same height it was dropped from. (Today, this is known to be the result of conservation of energy.) Galileo reasoned that if the second ramp were removed entirely, and the ball rolled down the first ramp and onto a flat surface, it would never be able to reach the height it was dropped from, and would therefore never stop moving if conditions were ideal. Galileo was essentially the first person to propose the idea that we now know as Newton's first law.		<b>Galileo Galilei (1564-1642)</b>, who studied the motion of celestial bodies, was the first to propose that perpetual motion was actually the natural state of objects, and that forces such as friction were necessary to bring them to rest or otherwise change their velocities. Galileo performed an experiment with two ramps and a bronze ball. The two ramps were set up at the same angle of incline, facing each other. Galileo observed that if a ball was released on one of the ramps from a certain height, it would roll down that ramp and up the other and reach that same height. He then experimented with altering the angle of the second ramp. He observed that even when the second ramp was less steep than the first, the ball would reach the same height it was dropped from. (Today, this is known to be the result of conservation of energy.) Galileo reasoned that if the second ramp were removed entirely, and the ball rolled down the first ramp and onto a flat surface, it would never be able to reach the height it was dropped from, and would therefore never stop moving if conditions were ideal. Galileo was essentially the first person to propose the idea that we now know as Newton's first law.

	Isaac Newton (1643-1727) confirmed Galileo's idea with his own experiments and published it along with his 2 other laws in his 1687 work <i>Principia Mathematica</i>. Newton refined Galileo's concept by expanding it to add that objects at rest will stay at rest, unless acted upon by a force. Although he gave credit to Galileo, today the law is known by Newton's name.		Isaac Newton (1643-1727) confirmed Galileo's idea with his own experiments and published it along with his 2 other laws in his 1687 work <i>Principia Mathematica</i>. Newton refined Galileo's concept by expanding it to add that objects at rest will stay at rest, unless acted upon by a force. Although he gave credit to Galileo, today the law is known by Newton's name.

Hnhan3: /* History */

2025-12-03T03:54:07Z

History

← Older revision		Revision as of 23:54, 2 December 2025
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	Galileo Galilei (1564-1642), who studied the motion of celestial bodies, was the first to propose that perpetual motion was actually the natural state of objects, and that forces such as friction were necessary to bring them to rest or otherwise change their velocities. Galileo performed an experiment with two ramps and a bronze ball. The two ramps were set up at the same angle of incline, facing each other. Galileo observed that if a ball was released on one of the ramps from a certain height, it would roll down that ramp and up the other and reach that same height. He then experimented with altering the angle of the second ramp. He observed that even when the second ramp was less steep than the first, the ball would reach the same height it was dropped from. (Today, this is known to be the result of conservation of energy.) Galileo reasoned that if the second ramp were removed entirely, and the ball rolled down the first ramp and onto a flat surface, it would never be able to reach the height it was dropped from, and would therefore never stop moving if conditions were ideal. Galileo was essentially the first person to propose the idea that we now know as Newton's first law.		Galileo Galilei (1564-1642), who studied the motion of celestial bodies, was the first to propose that perpetual motion was actually the natural state of objects, and that forces such as friction were necessary to bring them to rest or otherwise change their velocities. Galileo performed an experiment with two ramps and a bronze ball. The two ramps were set up at the same angle of incline, facing each other. Galileo observed that if a ball was released on one of the ramps from a certain height, it would roll down that ramp and up the other and reach that same height. He then experimented with altering the angle of the second ramp. He observed that even when the second ramp was less steep than the first, the ball would reach the same height it was dropped from. (Today, this is known to be the result of conservation of energy.) Galileo reasoned that if the second ramp were removed entirely, and the ball rolled down the first ramp and onto a flat surface, it would never be able to reach the height it was dropped from, and would therefore never stop moving if conditions were ideal. Galileo was essentially the first person to propose the idea that we now know as Newton's first law.

	Isaac Newton (1643-1727) confirmed Galileo's idea with his own experiments and published it along with his 2 other laws in his 1687 work <i>Principia Mathematica</i>. Although he gave credit to Galileo, today the law is known by Newton's name.		Isaac Newton (1643-1727) confirmed Galileo's idea with his own experiments and published it along with his 2 other laws in his 1687 work <i>Principia Mathematica</i>. Newton refined Galileo's concept by expanding it to add that objects at rest will stay at rest, unless acted upon by a force. Although he gave credit to Galileo, today the law is known by Newton's name.

	Newton's first law appears in <i>Principia</i> (which was written in Latin) as follows:		Newton's first law appears in <i>Principia</i> (which was written in Latin) as follows:
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	"Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed."		"Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed."

			Newton continued experimenting and found many fundamental ideas used in modern Physics today.

	==See Also==		==See Also==

Hnhan3: /* How It Originated */

2025-12-03T03:48:32Z

How It Originated

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	This law is an extension of the works of Galileo. Galileo developed the idea that an object would stay in motion linearly at a constant speed unless a force acts on it. Newton enhanced this concept by also adding that objects at rest will stay at rest unless acted upon by an unbalanced force.		This law is an extension of the works of Galileo. Galileo developed the idea that an object would stay in motion linearly at a constant speed unless a force acts on it. Newton enhanced this concept by also adding that objects at rest will stay at rest unless acted upon by an unbalanced force.

			Newton defined this force as proportional to the acceleration of the object. As an action is being exerted onto an object, it will change the objects state. Systems and bodies change their state of motion through interactions with their surroundings.

	===A Mathematical Model===		===A Mathematical Model===