How Do You Calculate Average Angular Acceleration?

[vysero]

Homework Statement

A rolling wheel moving to the right initially has an angular speed of 7.0 rad/s but after making 3
complete revolutions the wheel has a final angular speed of 11.0 rad/s. What is the magnitude and direction of the average angular acceleration of the wheel?

Homework Equations

(w2-w1)/(t2-t1) or maybe I need to use that equation and some rotational kinematics equations, not positive.

The Attempt at a Solution

I tried saying my time was 3 seconds but I am having trouble identifying the time. Not really sure where to start with this problem.

 

[Simon Bridge]

The wheel makes 3 complete revolutions ... so the angular displacement is:
You are right, you need kinematics. You know initial velocity, final velocity, and displacement: what is the equation that gives you the acceleration (hint: it does not have time in it)?

 

[vysero]

Awesome ty,

11^2 = 7^2 +2a(6pi)
a = 6pi

 

[vysero]

New question, well a continuation question:

For the speeds given in problem #6 above, what is the ratio of the wheel‟s final angular
momentum to the initial angular momentum?

L = rmvsin(theta)

I know the answer is 1.6 which is 11/7 however, I am not sure why that is. The question gave me a change in theta of 6pi and two speeds. Okay, so wouldn't dividing the speeds give you the ratio of the initial speed and final speed, not the momentum? Or is the speed also the momentum? I am confused.

 

[haruspex]

a = 6pi

Not quite. Try that last step again.

For the speeds given in problem #6 above, what is the ratio of the wheel‟s final angular
momentum to the initial angular momentum?

L = rmvsin(theta)

I know the answer is 1.6 which is 11/7 however, I am not sure why that is. The question gave me a change in theta of 6pi and two speeds. Okay, so wouldn't dividing the speeds give you the ratio of the initial speed and final speed, not the momentum? Or is the speed also the momentum?

angular momentum = moment of inertia * angular velocity, right?
Has the moment of inertia changed?

 

[Simon Bridge]

Awesome ty,

11^2 = 7^2 +2a(6pi)
a = 6pi

It helps to do the algebra before subbing in the numbers. So you are starting from: $\omega_f^2=\omega_i^2+2\alpha\theta$ and you want to solve for $\alpha$.

New question, well a continuation question:

For the speeds given in problem #6 above, what is the ratio of the wheel‟s final angular
momentum to the initial angular momentum?

The whole exercise is trying to get you to think in terms of angular thingies. So momentum is "normally" $p=mv$, and the "initial momentum" would be written $p_i=m_iv_i$ but if the mass does not change you just write $p_i=mv_i$ ... so, in angular stuff, it is: $L=I\omega$ ...

Remember to do the algebra before subbing in the numbers: - what is $L_f/L_i$?

 

[vysero]

So, Lf = IWf and Li = IWi? So, IWf/IWi = Wf/Wi?

 

[Simon Bridge]

So, Lf = IWf and Li = IWi? So, IWf/IWi = Wf/Wi?

Well done!

When a physics question asks for "the ratio between a and b" they usually want a/b.