Question

A rigid body is rotating counterclockwise about a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid body. If the object starts from rest at the initial angular position, moves counterclockwise with constant angular acceleration, and arrives at the final angular position with the same angular speed in all three cases, for which choice is the angular acceleration the highest?

* 3 rad, 6 rad

* 1 rad, 5 rad

* -1 rad, 1 rad

Answer 1

We know that angular acceleration will be highest in the case where the body covers the shortest angle since the angular speed at the final position in all three cases are same and we know that v² = u² +2*a*s where 'v' is the final angular speed 'u' is the initial angular speed 'a' is the angular acceleration and 's' is the angular displacement.

In our case the equation will be v² = 2*a*s since initial angular speed is 0.

above equation can also be written as a = v²/ 2s.

Since 'v' is constant for all the cases, so angular acceleration is inversely proportional to the angular displacement.

as we can see that the angular displacement is lowest in the case of '-1 rad, 1 rad' i.e 2 rad so this the correct answer