A) A child stands beside a 200 kg, 3 m merry-go-round. How much force must she e

Question

A) A child stands beside a 200 kg, 3 m merry-go-round. How much force must she exert tangent to the edge of the merry-go-round to spin it at 1 rev/s in 30 seconds?
B) If a merry-go-round exactly like the one mentioned in the previous problem was spinning at 1 rev/s and you dropped a 25 kg sand bag vertically onto the edge of the platform at a radius of 3 m, what would the new angular speed become?
C) An atwoods machine is made with masses M1 = 100 g, M2 = 120 g, and pulley mass of 100 g. What is the percent error in acceleration (relative to the correct formula) calculated by neglecting the pulley mass versus incorporating the pulley mass?

Explanation / Answer

A. The torque applied = moment of inertia * angular acceleration. since the force is constant, it is uniform acceleration so, F*R = I * (Ang Accn) equating , we get force as 10N. B. by applying conservation of angular momentum, (I1) W1 = (I1 + I2) W2 substuting the values, we get, new angular speed = 0.8 rev/s C.the accn without pulley mass is [m1 - m2 / m1 + m2]g the accn with pulley mass is [m1- m2 / m1 + m2 +( I/r^2)]g by substuting the values we get an error percentage of 17.7%. note that the radius term gets cancelled.

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