Question

A series of object are being rotated. The same net torque is being applied to each object. Rank the object in order of the resulting angular acceleration (1=lowest).

( ) A solid disk spinning about its center. Total mass is 0.5M and the radius is 2R.

( )An object consisting of two objects connected by a massless rod. Each object has a mass of 2M and is a distance R from the axis of rotation.

( )A solid disk spinning about its center. Total mass is M and a radius of R.

( )A hoop spinning about its center. Total mass is 2M and a radius of R.

Answer 1

We have to arrange in increasing order of =angular acceleration,given that =torque is same for each object

since,

Where   is the moment of inertia.since the is fixed so on decreasing the value of the value of will increase or we can say that less is the value of moment of inertia more is the angular acceleration .

Now,check moment of inertia of a solid disc about its center;

Given that ,

So,

Now, check moment of inertia,object consisting two objects as shown in figure 2.

Where,,,

So,

Now, solid disc spinning about its center.

Given that,,.

so

Now hoop spinning about its center

Where ,

So,

From above we conclude

so,