00:03
In this problem, two equal magnitude of torques are applied in two different objects, first on hollow cylinder and second on solid sphere.
00:13
The axis of rotation of hollow cylinder is the axis of symmetry about which it is going to rotate and the second one has the diameter.
00:24
So we have to determine which will have greater angular speed after a given time.
00:29
So how to calculate what will be our approach? so, velocity, angular velocity will be greater for that one or that object which will have greater acceleration.
00:41
So we have to first find which have greater angular acceleration.
00:47
Now we know that torque is equals to i into alpha.
00:51
So i is the moment of inertia and alpha is the angular acceleration.
00:57
In the given problem it is given that torque is equal for both of this object.
01:01
Therefore, moment of inertia of the cylinder into alpha of the cylinder should be equals to moment of inertia of a sphere into alpha of sphere.
01:12
Now what is the moment of inertia for the cylinder? so hollow cylinder has moment of inertia mr square, while solid sphere has moment of inertia 2 by 5 mr square.
01:25
So we can put these values here...