A 55 kg block is hanging from a rope that is wrapped around

A 5.5 kg block is hanging from a rope that is wrapped around the outside of a 13kg flywheel (disk) with a radius of 33cm that is hanging from the ceiling. Friction in the flywheel provides a constant torque of 2.5 Nm. When the block is rleased, what will be its acceleration as it falls?

Answer is supposed to be 3.9m/s^2. Explain Please.

Solution

Here ,

m1 = 5.5 Kg

m2 = 13 Kg

radius , r = 33 cm = 0.33 m

T = 2.5 N.m

let the acceleration is a

Using second law of motion

a = (m1 * g - T/r)/(m1 + 0.5 * m2 * r^2/r^2)

a = (5.5 * 9.8 - 2.5/.33)/(5.5 + 0.5 * 13)

a = 3.9 m/s^2

the acceleration of the system is 3.9 m/s^2