Question

Aliens are observing a park in new york. They notice a merry-go-round has a radius of 3.12m and a moment of inertia of 3100kgm^2 at the vertical axis through the center. The contraption has been lubricated recently so there is no friction. one of the earthlings applies a tangential force of 19N for 13s begging at rest. Unfortunaley after gathering this data the aliens computer broke so now they must calculate the work that was done over the course of the 13s.

Answer 1

Force applied = F = 19 N, Radius of the wheel ( of merry - go - round ) = R = 3.12 m,

Moment of intertia of it = I = 3100 kg . m / s².

Let the angular acceleration be .

Hence, torque applied = = F x R = I x

or, = FR / I = ( 19 x 3.12 ) / 3100 rad / s²

or, = 0.02 rad / s².

Initial angular velocity = 0 rad / s.

Hence, final angular velocity after t = 13 s : = x t = ( 0.02 x 13 ) rad / s = 0.26 rad / s.

Hence, work done in this 13 s : W = Change in rotational kinetic energy ( from work - energy theorem )

or, W = Final kinetic energy - Initial kinetic energy = ( I² / 2 ) - 0

or, W = ( 3100 x 0.26² / 2 ) J = 104.78 Joule.