Angular Momentum - Wheel with unequal radius

AI Thread Summary
The discussion revolves around a physics problem involving two objects attached to wheels with unequal radii, requiring the calculation of mass and angular acceleration. For part (a), the user correctly applied the net torque equation to find the mass m2 needed for no angular acceleration, using the given moment of inertia and radii. In part (b), the user initially miscalculated the angular acceleration after adding mass, failing to account for the effect of acceleration on tension in the ropes. A response clarified that the tensions differ from the weights when the system is accelerating, leading to the user's realization of the mistake. The conversation emphasizes the importance of understanding torque and tension in rotational dynamics.
Borat321
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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?
 
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Borat321 said:
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.
 
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Thanks - I got it!
 
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