A series of object are being rotated. The same net torque is being applied to ea

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 resultant angular acceleration (1=lowest).
1. A solid disk spinning about its center. Total mass is 0.5M and the radius is 2R.
2. A hoop spinning about its center. Total mass is 2M and a radius of R.
3. 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.
4. A solid disk spinning about its center. Total mass is M and a radius of R.

Explanation / Answer

we know thattorque=I* alpha ,

M.O.I .of 1) MR^2 / 2 = .5M * (2R)^2 / 2 = MR^2,

2.) 2M*R^2= 2MR^2 ,

3.) 2* 2M*R^2 = 4MR^2 ,

4.) MR^2 /2 ,

TORQUE IS SAME SO ALPHA IS INVERSLY PROPORTIONAL TO INERTIA ,

inertia , 3>2>1>4,

so angular acc. , 4>1>2>3

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