Q.84. Physics Laws of motion applied to rotational motion

Question 84.
A pulley has a radius of 2.70 m and a moment of inertia of 39.0 kg.m^2. A hanging mass is 4.20 kg and it exerts a force tangent to the edge of the pulley. What is the angular acceleration of the pulley?

Answer 84.
Let T = tension in the rope
and a = downward acceleration of the hanging mass

=>
mg - T = ma = mRα ... ( 1 ) for the hanging mass
T*R = Iα
=> T = Iα/R ... ( 2 ) for the pulley

Adding equations ( 1 ) and ( 2 ),
mg = mRα + Iα/R
=> α
= (mg) / (mR + I/R)
= (4.2 * 9.81) / (4.2*2.7 + 39/2.7)
= 1.6 rad/s^2.

LINK to YA!