Torque and Acceleration question

[veronicak5678]

Homework Statement

A solid wheel (I = 1/2 MR^2) initially rotating at 5 rad/s comes to a stop after 8 rotations.
a) Angular acceleration?
b) Tangential accelration at the rim?
c) If the mass is 2 kg and the radius is 1.5 m, find the net torque.
d) Using values form c, how much energy was required to bring the wheel to a stop?

Homework Equations

The Attempt at a Solution

a) -24.9 rad/s^2

b) -37.4 m/s^2

c) -56 Nm

d) I am not sure how to find the energy used.

 

[gabbagabbahey]

part(a) is incorrect and that error propagates through to (b) and (c)...perhaps you should show me how you got part (a)...

 

[veronicak5678]

For part a I used (w for omega for tangential velocity, a for alpha for angular acceleration )

w final ^2 - w initial^2 = 2a delta angle

(0 - (50 rad /s)^2 ) / (2 (50.3rad))

= -24.9 rad /s^2

 

[gabbagabbahey]

Your original post said the w_initial=5rad/s not 50...if it is 50 then your original answer is correct.

As for the energy required to stop the wheel; it should be the same as the 'work done by the torque' over an angular distance of 8*2pi...does that help?

 

[veronicak5678]

Sorry for the typo!

So the energy used will be 8* 2pi (-56.0Nm) ?