Question

Use the concept of conservation of angular momentum to explain the
following observations: (you should lean heavily on carefully drawn diagramS for these
explanations!)
a) You are sitting on a rotating chair. Somebody hands you a spinning bicycle wheel with
the axle horizontal. If you tip the wheel to one side, you and the chair start to rotate in
one direction. If you tip the wheel to the other side, you and the chair rotate in the other
direction.
b) The above spinning wheel has an axle that extends a few centimeters from the wheel.
You can hang the spinning wheel from the end of the axle and the wheel will stay upright!
What happens to the wheel as it is hanging?
c) A cat is dropped from a safe height (2 meters or so) onto a frying pan . . . which is cold
and has a cushion on top of it! Even though the cat is dropped from rest while upside down
(with zero angular momentum!!), it is able to spin itself and land on it’s own four feet.
d) You are now a professional disc golfer. You throw a disc as shown here:

www.youtube.com/watch?v=x3K53OqEOZg

The disc starts off with the left side tilted down. As it flies, the left side of the disc rotates
up and the right side rotates down until the left and right sides are even and the disc is
level.

(You don’t need to explain what happens after the disc reaches level flight. The disc eventu-
ally tilts back the other direction, which has to do with the disc slowing down, descending, and the center of pressure shifting among other things)

A hint: the front of the disc is higher than the back of the disc, this causes the center of
pressure (what is this?) to be a little behind the center of rotation of the disc, causing a
torque. Also, which way is the disc spinning!?

Answer 1

Ans a)

Since I am holding the rotating wheel with the tip on one side of the chair, therfore the force developed by the rotating wheel makes a torque about the axis of the rotating chair. Inorder to balance the angular momentum of the whole system, the chair starts to rotate about its axis in the direction depending upon the direction of rotation of the wheel.

Ans b)

When the wheel is rotated about its axis and made to hang from end of the axle, the wheel will keep on rotating with the axle being horizontal and the circumfrence of the wheel being vertical. This phenomenon will continue as long as the wheel keeps on rotating. The reason behind this is Inertia. When at a particular moment the top part of the wheel wants to lean to come down due to action of gravitaional force, the next moment it rotates and come on the downward part of the wheel thus gyroscopic effect comes to play which keeps the wheel upright.

Ans c)

This happens because cats have the ability to twist themselves to face downward even without changing their net angular momentum. They are able to do this by the following method in succession:

• They first bend their middle body part so that the front half of the body rotates in a different axis from the rear-half of the body.
• They tuck their front(or rear) legs to minimise the moment of inertia of the front( or rear) body. Simultaneously, they extend their rear(or front) legs to maximise the moment of inertia. This method enable the cats to rotate their one part of the body(either front or rear) as much as 90° while the other half of the body rotates only by a small degree like 10°.
• The cat repeats the above two steps till the it is facing downward.

Thus, the above phenomenon conserves the angular momentum.

Ans d)

As explained in "ans b" the gyroscopic effect comes to play when a disc is rotated. This gyrosocpic effect is responsible for making the tlted position of the disc to horizontal.

Clearly from the video we can see that the man is throwing the disc from "right hand" and the disc is deviating towards left ( few moments before it hits the ground) therefore we can conclude that the disc is rotating "clockwise" when viewed from the top.