Wong is standing on a turntable in class holding a weight in each hand a distance .75 meters from the center of his body. He is originally rotating with an angular frequency w=0.3 rad/s. He pulls the weights in so they are only .25 meters from the axis of rotation. The original moment of inertia of wong, the turntable and the weights is I,initial = 8kgm^2. The final moment of inertia of Wong, the turntable and the weights is I,final= 5kgm^2

Question

Wong is standing on a turntable in class holding a weight in each hand a distance .75 meters from the center of his body. He is originally rotating with an angular frequency w=0.3 rad/s. He pulls the weights in so they are only .25 meters from the axis of rotation. The original moment of inertia of wong, the turntable and the weights is I,initial = 8kgm^2. The final moment of inertia of Wong, the turntable and the weights is I,final= 5kgm^2

What is wong's final angular velocity W,final?

As justin pulls the weights in, the total angular momentum of wong, the turntable, and the weights

increases, decreases, or remains the same?

Answer 1

Please show some effort and we will critique your work.

This is clearly an conservation of angular momentum problem.

You are not going to learn anything if yuou expect us to do all the work for you.

Answer 2

ok formula L=Iw i know I=5kgm^2 and i am finding w. How would i go about finding L give me a hint.

Answer 3

To find Wong's final angular velocity, we can use the principle of conservation of angular momentum. According to this principle, the total angular momentum of a system remains constant unless acted upon by an external torque.

In this case, Wong is standing on a turntable and holding weights. Initially, Wong has an angular frequency w = 0.3 rad/s and a moment of inertia I_initial = 8 kgm^2. When Wong pulls the weights in, the moment of inertia decreases to I_final = 5 kgm^2.

The equation for conservation of angular momentum is:
L_initial = L_final

The initial angular momentum, L_initial, is given by:
L_initial = I_initial * w

The final angular momentum, L_final, is given by:
L_final = I_final * W_final

Setting the initial and final angular momentum equations equal to each other, we have:
I_initial * w = I_final * W_final

We can plug in the given values for moment of inertia and angular frequency to solve for W_final:
8 kgm^2 * 0.3 rad/s = 5 kgm^2 * W_final

Simplifying the equation, we have:
2.4 kgm^2/s = 5 kgm^2 * W_final

Now, we can solve for W_final:
W_final = 2.4 kgm^2/s / 5 kgm^2
W_final = 0.48 rad/s

Therefore, Wong's final angular velocity, W_final, is 0.48 rad/s.

Regarding the total angular momentum of Wong, the turntable, and the weights, as Wong pulls the weights in, the moment of inertia decreases. Since angular momentum is the product of moment of inertia and angular velocity, the total angular momentum decreases as well. Therefore, the total angular momentum of Wong, the turntable, and the weights decreases as the weights are pulled in.