Angular Momentum - Wheel with unequal radius

[Borat321]

I had the following question on webassign -

Two objects are attached to ropes that are attached to wheels on a common axle as shown in Figure 9-55. The two wheels are glued together so that they form a single object. The total moment of inertia of the object is 40 kgm2. The radii of the wheels are R1 = 1.2 m and R2 = 0.4 m.

http://www.physics.louisville.edu/wkomp/teaching/summer2005/p298/quizzes/quiz4.pdf

It's #3 - I couldn't attach it.

Find:
(a) If m1 = 24 kg, find m2 such that there is no angular acceleration of the wheels.
(b) If 12 kg is gently added to the top of m1, find the angular acceleration of the wheels.

It's problem 18 - I got part a by doing the net torque=Ia, so (M1gr1)-(m2gr2)=0, and solved for m2.

For part B, I thought you could do it by plugging in 40 for I and plugging the rest of the numbers (adding 12 to M1, of course and getting a, but it seems to be wrong - can anyone tell me why?

 

[OlderDan]

I had the following question on webassign -

Two objects are attached to ropes that are attached to wheels on a common axle as shown in Figure 9-55. The two wheels are glued together so that they form a single object. The total moment of inertia of the object is 40 kgm2. The radii of the wheels are R1 = 1.2 m and R2 = 0.4 m.

http://www.physics.louisville.edu/wkomp/teaching/summer2005/p298/quizzes/quiz4.pdf

It's #3 - I couldn't attach it.

Find:
(a) If m1 = 24 kg, find m2 such that there is no angular acceleration of the wheels.
(b) If 12 kg is gently added to the top of m1, find the angular acceleration of the wheels.

It's problem 18 - I got part a by doing the net torque=Ia, so (M1gr1)-(m2gr2)=0, and solved for m2.

For part B, I thought you could do it by plugging in 40 for I and plugging the rest of the numbers (adding 12 to M1, of course and getting a, but it seems to be wrong - can anyone tell me why?

You are probably forgetting about the acceleration of the masses. In part a, the tensions in the strings were the weights of the two masses. When the masses are accelerating, the tensions are not the weights.

 

[Borat321]

Thanks - I got it!