Try these "busters" to exercise your brain ... they should help you grasp the concepts underlying rotational motion, angular momentum. To gain the maximum effect you should attempt to answer them before looking at the answers!
[1] At an amusement park you sit close to the outside of a large carousel that is allowed to rotate freely after it is set spinning. After a short while you begin to feel ill and decide to move towards the center of the carousel. As you make your way inwards does the rate of rotation increase, decrease or remain the same? Explain your answer.
[2] A sizeable amount of dirt is washed down the Mississippi River and deposited in the Gulf of Mexico every year. What effect does this tend to have on the length of the day?
[3] (Funny one ... this!) How would the length of the day be affected if the whole population of the Earth walked in an easterly direction? What about when they stopped walking?
[4] A radio-controlled toy car runs on a track fixed to a horizontally oriented bicycle wheel that is free to rotate.
If everything is stationary, initially, what is the response of the bicycle wheel when the car starts to move forward, i.e., clockwise? What about when it is set in reverse? How do the resultant motions depend on the relative masses of the wheel and the car, i.e., what happens if the car: (a) is more massive, (b) is less massive, or (c) has the same mass, as the wheel?
[5] Why does a helicopter, like the one shown below, have a second, small rotor fixed close its tail? Describe what would happen if the second rotor fails.
[6]
A small ball is resting against a rod that is fixed radially to a disk (lying in the horizontal plane). When the disk rotates, the ball with move along the rod towards the circumference of the disk, (a). At the instant the ball reaches the end of the rod and becomes "free", (b), which path A, B, C or D does the it follow?
[7] As the Earth rotates under the tidal bulges, which are produced by the Moon, there is a frictional force between the water and the Ocean floor. One consequence is that the Earth's rotation slows and the days are getting longer (by something like 0.0015s per century!). That means the angular momentum of the Earth is getting smaller. Angular momentum can change providing there's an external torque acting on the system; but in the Earth-Moon case there is no external torque. So, how is the total momentum of the Earth-Moon system conserved?
[8] When you turn a corner in your car, the 'outside' wheels rotate more quickly than the 'inner' wheels ... if they didn't, for example, if they were connected by a rigid axle, then either the inner or outer pairs would skid. Clearly, that doesn't happen. So, can you explain how the inner and outer wheels are free to rotate at different rates?
[9] Spin an egg on a table top, stop it briefly with your finger, and quickly release it again. A cooked egg will remain at rest, but an uncooked egg will start to rotate again! Why?
[10] You are piloting a small propellor driven airplane; to you, the propellor is rotating counter-clockwise. To take-off you have to raise the nose of the airplane. As you do so, the airplane tends to turn to one side. Which way does it tend to turn and why?
While you are flying level, you make a turn to the right. Again the airplane tends to move in a different direction ... which way?
[11] (This is a famous problem similar to one that troubled Nobel Laureate Richard Feynman many years ago!) A can, filled with water, has four holes in it; the holes are punched in such a way that the water flows out approximately tangentially to the sides of the can. If the can is supported by fine strings and released from rest ...
... it rotates, shown above (a). The first question is why does the can rotate?
If, instead, the (empty) can is suspended in a bucket of water, as shown in (b), water flows in through the holes. The second question is ... what will happen when the can is released from rest? Will the can rotate in the same direction as before, in the opposite direction or not rotate at all? Why?
[12] (This is not a trick question but does require a little thought!) An object is attached to a string that passes through a hole in a frictionless, horizontal surface. A force is applied at the lower end of the string to keep the object rotating in a circle of constant radius, as shown below.
If the force is increased, the radius of the orbit decreases and the speed of the object increases. This increase in speed is an acceleration ... but how can the increased force ... applied through the string radially ... change the tangential speed of the object?