00:01
In this problem we have a pulley of mass 1 .5 kilograms and diameter 0 .9 meter.
00:12
Now a spring is wrapped around the pulley and the other end is attached to a hanging mass of 8 kilograms.
00:22
The system is released from rest we have to find out the acceleration of the hanging mass, the tension in the string and the moment of inertia for the pulley about the axis of rotation that is to its center.
00:38
The moment of inertia equals half times mass of the pulley times square of the radius or it equals half times mass times d square over 4.
00:50
So the moment of inertia equals half times 1 .5 kilograms times 0 .9 meters square over 4.
01:01
The moment of inertia of the pulley equals 0 .152 kilogram meter square.
01:10
Now to find out the tension and the acceleration we need to draw the free body diagram.
01:15
The weight of the hanging mass mg act in the vertical downward direction.
01:20
The tension t pulls the hanging mass in upward direction.
01:25
Now the same amount of tension pulls the pulley in the downward direction.
01:32
The angular acceleration of the pulley is alpha and the linear acceleration we have assumed from the hanging mass is a...