A357 kg merry-go-round in the shape of a horizontal disk with a radius of 2 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. how large a torque would have to be exerted to bring the merry-go-round from rest to an angular speed of 4.3 rad/s in 2.8 s

Torque,

Explanation:

It is given that,

Mass of the merry go round, m = 357 kg

Radius of the horizontal disk, r = 2 m

Initial speed of the merry go round,

Final angular speed,

Time, t = 2.8 s

It is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. We need to find how large a torque would have to be exerted to bring the merry-go-round from rest to an angular speed of 4.3 rad/s in 2.8 s. It is given by :

I is the moment of inertia of the disk,

is the angular acceleration

So, the torque exerted is 1096.5 N-m. Hence, this is the required solution.