Physics rotational motion question


A small gear with mass m and radius r is free to rotate about its central axis.
A force is applied to an interior hub, at a radial distance r/2 from the axis.
a) What is the angular acceleration of the small gear resulting from the a1.jpg pplied force?
Take the moment of inertia of the gear to be that of a cylinder.
b) If a force of 4N, is applied for 10s, what will be the angular velocity of the small
gear, assuming it starts at rest? (be sure to indicate its direction)
c) Once, reaching this speed, the small gear is engaged with a larger gear, of mass
4m, and radius 4r. If the angular speed of the small gear is maintained, what is the
angular velocity of the larger gear, assuming there is no slipping?
d) What is the total kinetic energy of the system at this point?

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