Object on Rotating Merry-Go-Round · USAPhO 2010 #A1
Physics · mechanics
Problem
An object of mass m is sitting at the northernmost edge of a stationary merry-go-round of radius R. The merry-go-round begins rotating clockwise (as seen from above) with constant angular acceleration of α. The coefficient of static friction between the object and the merry-go-round is µs.
a. Derive an expression for the magnitude of the object's velocity at the instant when it slides off the merry-go-round in terms of µs, R, α, and any necessary fundamental constants.
b. For this problem assume that µs = 0.5, α = 0.2 rad/s², and R = 4 m. At what angle, as measured clockwise from north, is the direction of the object's velocity at the instant when it slides off the merry-go-round? Report your answer to the nearest degree in the range 0 to 360°.