Question

At a playground you let your kid sister (30 kg) kneel on the surface (near the edge) of a 2 meter diameter merry-go-round, of mass 300 kg. You push the merry-go-round along the edge, so that it constantly accelerates from rest to a final speed of 1.5 rotations per second at the end of a 20 sec interval. Friction is negligible. b) How much force did you apply in the direction tangent to the circumference of the merry-go-round, at the point of contact (in Newtons), during the 20 sec time interval? c) After it comes up to speed, you stop pushing and the merry-go-round continues to run at a constant rate of 1.5 rotations per second (remember that we are neglecting friction). What is the magnitude and direction of your sister’s acceleration, if any? d) Your kid sister now walks across the center of the merry-go-round, to a point a distance 0.5 meters from the center “on the other side”. What is the new angular velocity of the merry-go-round (in rad/sec) when she is 0.5 meters from the center “on the other side”? e) For a rigid body undergoing rotation, write down a symbolic expression for its rotational kinetic energy, in terms of the magnitude of its angular momentum L, and its moment of inertia I about the rotation axis. f) What is the total change in the kinetic energy of the merry-go-round, including your sister, as a result of her walk (in Joules)? g) In the part of her walk from the center to the other side: (i) is the change in kinetic energy of the merry-go-round (including your sister) positive or negative? Explain. (ii) is the change in your sister’s kinetic energy positive or negative? Explain.

Answer 1