Torque - Revision history

Rayedc: /* Solution: */

2024-12-03T22:56:07Z

Solution:

← Older revision		Revision as of 18:56, 3 December 2024
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	disk = cylinder(pos=vector(0,0,0), axis=vector(0,0.01,0), radius=0.5, color=color.blue)		disk = cylinder(pos=vector(0,0,0), axis=vector(0,0.01,0), radius=0.5, color=color.blue)
	pivot = sphere(pos=vector(0,0,0), radius=0.02, color=color.red)		pivot = sphere(pos=vector(0,0,0), radius=0.02, color=color.red)

	# Physical Properties		# Physical Properties
	M = 2 # Mass in kg		M = 2 # Mass in kg
	R = 0.5 # Radius in meters		R = 0.5 # Radius in meters
	I = 0.5 * M * R**2 # Moment of inertia for a solid disk		I = 0.5 * M * R**2 # Moment of inertia for a solid disk

	# Applied Force		# Applied Force
	F = 5 # Force in Newtons		F = 5 # Force in Newtons
	tau = R * F # Torque = r x F		tau = R * F # Torque = r x F
	alpha = tau / I # Angular acceleration		alpha = tau / I # Angular acceleration

	# Initial Conditions		# Initial Conditions
	theta = 0 # Initial angle		theta = 0 # Initial angle
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	t = 0 # Time		t = 0 # Time
	dt = 0.01 # Time step		dt = 0.01 # Time step
			# Simulation Loop
	# Simulation Loop		while t < 5:
	while t < 5:		rate(100)
	rate(100)		# Update angular velocity and angle
	# Update angular velocity and angle		omega += alpha * dt
	omega += alpha * dt		theta += omega * dt
	theta += omega * dt

	# Rotate the disk		# Rotate the disk
	disk.rotate(angle=omega*dt, axis=vector(0,0,1), origin=pivot.pos)		disk.rotate(angle=omega*dt, axis=vector(0,0,1), origin=pivot.pos)

	# Advance time		# Advance time
	t += dt		t += dt

	==Connectedness==		==Connectedness==

Rayedc: /* Solution: */

2024-12-03T22:55:29Z

Solution:

← Older revision		Revision as of 18:55, 3 December 2024
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	GlowScript 3.0 VPython		GlowScript 3.0 VPython

	# Visualization		# Visualization
	disk = cylinder(pos=vector(0,0,0), axis=vector(0,0.01,0), radius=0.5, color=color.blue)		disk = cylinder(pos=vector(0,0,0), axis=vector(0,0.01,0), radius=0.5, color=color.blue)
	pivot = sphere(pos=vector(0,0,0), radius=0.02, color=color.red)		pivot = sphere(pos=vector(0,0,0), radius=0.02, color=color.red)

	# Physical Properties		# Physical Properties
	M = 2 # Mass in kg		M = 2 # Mass in kg
	R = 0.5 # Radius in meters		R = 0.5 # Radius in meters
	I = 0.5 * M * R**2 # Moment of inertia for a solid disk		I = 0.5 * M * R**2 # Moment of inertia for a solid disk

	# Applied Force		# Applied Force
	F = 5 # Force in Newtons		F = 5 # Force in Newtons
	tau = R * F # Torque = r x F		tau = R * F # Torque = r x F
	alpha = tau / I # Angular acceleration		alpha = tau / I # Angular acceleration

	# Initial Conditions		# Initial Conditions
	theta = 0 # Initial angle		theta = 0 # Initial angle
	omega = 0 # Initial angular velocity		omega = 0 # Initial angular velocity
	t = 0 # Time		t = 0 # Time
	dt = 0.01 # Time step		dt = 0.01 # Time step

	# Simulation Loop		# Simulation Loop
	while t < 5:		while t < 5:
	rate(100)		rate(100)
	# Update angular velocity and angle		# Update angular velocity and angle
	omega += alpha * dt		omega += alpha * dt
	theta += omega * dt		theta += omega * dt

	# Rotate the disk		# Rotate the disk
	disk.rotate(angle=omega*dt, axis=vector(0,0,1), origin=pivot.pos)		disk.rotate(angle=omega*dt, axis=vector(0,0,1), origin=pivot.pos)

	# Advance time		# Advance time
	t += dt		t += dt

	~~This Python snippet, when evaluated, will show that~~
	~~<math>\Delta E_{internal} = 5175 J</math>.~~

	==Connectedness==		==Connectedness==

Rayedc: /* Solution: */

2024-12-03T22:53:51Z

Solution:

@@ Line 169: / Line 169: @@
 [[File:Trqb2.png|center]]
 <div></div>
 ==Connectedness==

Rayedc: /* Solution: */

2024-12-03T22:50:12Z

Solution:

← Older revision		Revision as of 18:50, 3 December 2024
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	Using Newton's second law for rotation:		Using Newton's second law for rotation:
	<div></div>		<div></div>
	[[File:Trqb2.~~pngcenter~~]]		[[File:Trqb2.png\|center]]
	<div></div>		<div></div>

Rayedc: /* Solution: */

2024-12-03T22:50:00Z

Solution:

← Older revision		Revision as of 18:50, 3 December 2024
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	<div></div>		<div></div>
	[[File:Trqb.png\|center]]		[[File:Trqb.png\|center]]
			<div></div>

			Using Newton's second law for rotation:
			<div></div>
			[[File:Trqb2.pngcenter]]
	<div></div>		<div></div>

Rayedc: /* Solution: */

2024-12-03T22:45:34Z

Solution:

← Older revision		Revision as of 18:45, 3 December 2024
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	<div></div>		<div></div>
	[[File:TorquePart1.png\|center]]		[[File:TorquePart1.png\|center]]
			<div></div>

			b) Determining Angular Acceleration (𝛼)

			The moment of inertia for a solid disk in this case:
			<div></div>
			[[File:Trqb.png\|center]]
	<div></div>		<div></div>

Rayedc: /* Problem 1 */

2024-12-03T22:41:59Z

Problem 1

← Older revision		Revision as of 18:41, 3 December 2024
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	c) Use Glowscript to simulate the rotational motion of the disk over 5 seconds.		c) Use Glowscript to simulate the rotational motion of the disk over 5 seconds.

	Solution:		====Solution:====

	a) Calculating Torque (τ)		a) Calculating Torque (τ)

Rayedc: /* Problem 1 */

2024-12-03T22:40:34Z

Problem 1

← Older revision		Revision as of 18:40, 3 December 2024
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	===Problem 1===		===Problem 1===
	Rotating Disk:		====Rotating Disk:====

	A solid disk with a mass of 2 kg and a radius of 0.5 m is initially at rest. A constant tangential force of 5 N is applied at the edge of the disk.		A solid disk with a mass of 2 kg and a radius of 0.5 m is initially at rest. A constant tangential force of 5 N is applied at the edge of the disk.
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	[[File:TorquePart1.png\|center]]		[[File:TorquePart1.png\|center]]
	<div></div>		<div></div>

	==Connectedness==		==Connectedness==
	Torque exists almost everywhere we go and is involved in nearly everything we do. If torque didn't exist, we would only be able to do things linearly in a uniform line and there wouldn't be spin, turn, or circular motion. Actions such as turning a steering wheel or opening a bottle would be impossible without the twisting motion we call torque.		Torque exists almost everywhere we go and is involved in nearly everything we do. If torque didn't exist, we would only be able to do things linearly in a uniform line and there wouldn't be spin, turn, or circular motion. Actions such as turning a steering wheel or opening a bottle would be impossible without the twisting motion we call torque.

Rayedc at 22:39, 3 December 2024

2024-12-03T22:39:40Z

← Older revision		Revision as of 18:39, 3 December 2024
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	<div></div>		<div></div>
	[[File:finalnettorque.png\|center]]		[[File:finalnettorque.png\|center]]


	For a brief introduction on a different method of calculating cross products (using matrices and cofactor expansion), watch this video:		For a brief introduction on a different method of calculating cross products (using matrices and cofactor expansion), watch this video:
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	<div></div>		<div></div>

			Since the force is applied tangentially at the edge,

			<div></div>
			[[File:TorquePart1.png\|center]]
			<div></div>
	==Connectedness==		==Connectedness==
	Torque exists almost everywhere we go and is involved in nearly everything we do. If torque didn't exist, we would only be able to do things linearly in a uniform line and there wouldn't be spin, turn, or circular motion. Actions such as turning a steering wheel or opening a bottle would be impossible without the twisting motion we call torque.		Torque exists almost everywhere we go and is involved in nearly everything we do. If torque didn't exist, we would only be able to do things linearly in a uniform line and there wouldn't be spin, turn, or circular motion. Actions such as turning a steering wheel or opening a bottle would be impossible without the twisting motion we call torque.

Rayedc: /* Problem 1 */

2024-12-03T22:37:17Z

Problem 1

← Older revision		Revision as of 18:37, 3 December 2024
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	Torque is given by:		Torque is given by:
	<div></div>		<div></div>
	[[File:Torqueform~~.png~~.png\|center]]		[[File:Torqueform.png\|center]]
	<div></div>		<div></div>