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 resulting angular acceleration (1=lowest).

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

2. 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.

3. A solid sphere spinning about its center. Total mass is M and the radius is R.

4. A solid disk spinning about its center. Total mass is M and a radius of 2R.

Explanation / Answer

From the relation betweent Torque and moment of inertia and angular acceleration is

   Tau = I*alpha, Tau = Torque, I= moment of inertia, alpha = angular acceleration

here as the torque is same on all objects so the object with higher momentof inertia will have less angular acceleration.

   given objects are

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

   I1 = 1/2 MR^2 = 0.5 MR^2
2. 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.

   I2 = 2(2M)R^2 = 4MR^2

3. A solid sphere spinning about its center. Total mass is M and the radius is R.

   I3 = 2/5 MR^2 = 0.4 MR^2

4. A solid disk spinning about its center. Total mass is M and a radius of 2R.

   I4 = MR^2/2 = 1/2* M(2R)^2 =2MR^2

  
   I2 < I4 < I1 < I3

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