Angular Momentum - Wheel with unequal radius

In summary, the conversation discusses a question from webassign about two objects attached to ropes and wheels on a common axle. The total moment of inertia of the object is given and the radii of the wheels are provided. The question asks to find the mass of the second object when the first object has a mass of 24 kg and there is no angular acceleration, as well as the angular acceleration when 12 kg is added to the first object. The conversation also mentions a possible mistake in using the net torque formula and the reminder to consider the acceleration of the masses.
  • #1
Borat321
5
0
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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  • #2
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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  • #3
Thanks - I got it!
 

Related to Angular Momentum - Wheel with unequal radius

1. What is angular momentum?

Angular momentum is a property of a rotating object that describes how much rotational motion it possesses. It is defined as the product of the object's moment of inertia (a measure of its resistance to rotational motion) and its angular velocity (how fast it is rotating).

2. How is angular momentum related to the wheel with unequal radius?

In the context of the wheel with unequal radius, angular momentum is important because it is conserved, meaning it remains constant as long as no external torques act on the system. This means that the angular momentum of the wheel with unequal radius will remain the same even if the wheel speeds up or slows down due to changes in its radius.

3. What are the factors that affect the angular momentum of the wheel with unequal radius?

The angular momentum of the wheel with unequal radius is affected by two main factors: the moment of inertia and the angular velocity. The moment of inertia depends on the mass distribution and the shape of the wheel, while the angular velocity depends on the speed at which the wheel is rotating.

4. How does the unequal radius affect the angular momentum of the wheel?

The unequal radius of the wheel affects its angular momentum by changing its moment of inertia. The farther the mass is distributed from the center of rotation, the larger the moment of inertia will be. This means that a wheel with unequal radii will have a different angular momentum than a wheel with equal radii, even if they are rotating at the same speed.

5. Can the angular momentum of the wheel with unequal radius ever change?

As mentioned before, angular momentum is conserved in a closed system, meaning it will remain constant unless acted upon by an external torque. Therefore, the angular momentum of the wheel with unequal radius can only change if there is a torque acting on the system, such as friction or an external force.

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