00:02
Hello, in the question we have given two spheres each rotating at an angular speed.
00:07
So, omega initial is given to be 24 .5 radian per second about the axis that passes through their centers.
00:21
So, each of radius, so the radius is given that is equals to 0 .32 meters and the mass of 1 .32 kg.
00:42
However, in the figure one is solid and another is thin walled spherical shell.
00:49
Suddenly a net torque due to friction, the magnitude of the torque is given that is equals to 0 .39 newton meter is given, begins to act on each sphere and slows the motion down.
01:13
So, how long does it take for the solid sphere and the thin walled sphere to come to the halt? so, in order to do this, now we know that the torque, torque is given by tau is equals to i times alpha.
01:35
So, this is the relation between the torque and the angular acceleration and the moment of inertia.
01:45
So, from here this alpha will turn out to be tau divided by i.
01:51
So, we have an equation of motion that is omega final is equal to omega initial plus alpha t.
02:03
As it is slowing down, this alpha will be negative.
02:07
So, omega final is negative 0 because it is coming to halt that is equals to omega initial is 24 .5 minus this is i by tau alpha sorry it is tau alpha is tau by i.
02:32
So, this is tau by i times t.
02:35
So, if we rearrange this equation, so we will get t as equals to 2 point sorry 24 .5 times i divided by tau.
02:52
So, tau value also we can put.
02:55
So, that will be 24 .5 i divided by this tau is 0 .39...