Systems with Nonzero Torque

Claimed by nvohra3.

In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.

The Main Idea

With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence [math]\displaystyle{ \vec{L}_{final} = \vec{L}_{initial}. }[/math] See However, we're not always fortunate enough to have such systems.

A Mathematical Model

So the angular momentum principle is the following: [math]\displaystyle{ {\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} }[/math]

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Taken from WebAssign and/or Matters and Interactions: Fourth Edition

Simple

A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? A) Moment of inertia B) Center of mass C) Angular momentum D) Angular velocity E) Angular acceleration

Solution/Explanation: C, D. Why? A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. B) Center of mass doesn't change with applied torque as well. C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. D) Angular velocity changes since a constant force is being applied to the object, causing the object to E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!).

Middling

Difficult

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References

Matters and Interactions: 4th Edition