Most of us have seen a figure skater whose big spinning finale at the end of her

Question

Most of us have seen a figure skater whose big spinning finale at the end of her routine makes her into a veritable blur. At first, she's spinning at some reasonable rate, but then-with nobody giving her any kind of push to go faster, she's able to increase her rate of rotation a LOT. How does do that? Find out. Tab lab is short on ice rinks, but we do have a rotating chair. Have someone from your group-(someone who is not prone to motion sickness) climb aboard the chair. To accentuate the effect, have him/her take one of the weights in each hand and hold out his/her hands and also extend his/her legs straight out. Have everyone else back up, then one other team member give the volunteer a (gentle) turn-not very fast! After that person has finished accelerating the volunteer and has stepped back-assuming the chair's axle is has low friction (and ignoring the slow rotation of the earth), the volunteer and chair are essentially an isolated rotating body-like a figure skater spinning on slick ice. Let the volunteer go around a couple of times, then ask him/her to draw in his/her arms and legs...then extend them out again....What happens-and why? Answer by using the Conservation of Angular Momentum: Write an appropriate equation and rearrange it to make your point. (When the volunteer has had enough, be sure to stop the chair.) Now, let another volunteer from the group-someone with good arm strength-put on the gloves and sit in the chair. This time he/she should remain basically still. Then someone else should hold the bicycle wheel so that its axis is vertical and someone should give it a strong spin-get it going pretty good-clockwise, as viewed from above. Now, without changing the orientation of that axis, carefully give the spinning wheel to the person in the chair and stand back. That person should hold the bottom axis in one hand and use the other (gloved) hand to brush against the outside of the spinning wheel (don't catch any fingers in the spokes!), until the wheel is at rest against the glove. What happens? Why? Answer by using the Conservation of Angular Momentum: Write an appropriate equation and rearrange it to make your point. Predict: What would have happened if the bike wheel had been going counter clockwise instead of clockwise? Explain your prediction with an equation. Now test your prediction-repeat step b with the bike wheel going counter clockwise (as viewed from above). What happens? Predict: What will happen if the volunteer in the chair, holding the stopped bike wheel (always with its axis vertical) now gives it a strong push to start it turning again? Will direction matter? Explain your predictions with equations. Now test your prediction-once for each spinning direction. What happens? When land ice on Antarctica melts and flows into the sea, eventually it circulates and therefore distributes uniformly over the earth's oceans. As a result, does the earth's rotational speed increase, decrease or remain unaffected? (Does this change the length of one day? If so, how?) As always, explain your thinking fully.

Explanation / Answer

Here ,

a) as the angular momentum is given as

L = I * w

I is the moment of inertia

w is the angular speed .

as the volunteer draws hands in , the moment of interia will decrease

as the angular momentum is conserved, the angular speed will increase.

b)

here , as the angular momentum is conserved,

while holding the wheel ,

the person will start rotating in clockwise direction.

let the final angular speed is wf

using conservation of angular momentum

wf * (Iwheel + Iperson) = Iwheel * winitial

c)

let the final angular speed is wf

using conservation of angular momentum

wf * (Iwheel + Iperson) = Iwheel * winitial

for the counter clockwise direction

the person will rotate in counter clockwise direction

d)

as the angular momentum is contant

initial angular momentum is zero

Iperson * wperson + Iwheel * Wwheel = 0

hence , the person will start to rotate in oposite direction to that of wheel

person will rotate clockwise direction for counter clockwise

person will rotate counter clockwise direction for clockwise

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