Question

The L-shaped object(Figure 1) can be rotated in one of the following three ways: case A, about the x axis; case B, about the y axis; and case C, about the z axis (which passes through the origin perpendicular to the plane of the figure).

If the same torque ? is applied in each of these cases, rank them in decreasing order of the resulting angular acceleration.

The L-shaped object(Figure 1) can be rotated in one of the following three ways: case A, about the x axis; case B, about the y axis; and case C, about the z axis (which passes through the origin perpendicular to the plane of the figure). If the same torque ? is applied in each of these cases, rank them in decreasing order of the resulting angular acceleration.

Answer 1

We know that where τ is the torque. I is the moment of inertia and α is the angular acceleration As same torque is applied in each case, Which means angular acceleration is inversely proportional to moment of inertia. Case A When it is rotated about the x-axis, then only 9.0 kg sphere would contribute the moment of inertia. Calculate the moment of inertia about x-axis, Substitute the values 1,-9.0x(1.0) -9.0 kg-m Case B When it is rotated about the y-axis, then only 2.5 kg sphere would contribute the moment of inertia Calculate the moment of inertia about y-axis, Substitute the values

1,-25x(2.0) =10.0 kg-m Case C. When it is rotated about the z-axis, then only 2.5 kg and 9.0 kg spheres would contribute the moment of inertia. Calculate the moment of inertia about z-axis, Substitute the values. 1,-25x (20). +9.0x (1.0). -19.0 kg-m Therefore As the angular acceleration is inversely proportional to the moment of inertia for same torque, therefore, decreasing order of angular acceleration is