Ncert Exercises & Solutions

Q. 20 A wheel in uniform motion about an axis passing through its center and perpendicular to its plane is considered to be in mechanical (translational plus rotational) equilibrium because no net external force or torque is required to sustain its motion. However, the particles that constitute the wheel do experience a centripetal acceleration directed towards the center. How do you reconcile this fact with the wheel being in equilibrium?

How would you set a half wheel into uniform motion about an axis passing through the center of mass of the wheel and perpendicular to its plane? Will you require external forces to sustain the motion?

Hint: For mechanical equilibrium, net force and net torque should be zero.

Step 1: Interpret the motion of full wheel.

The wheel is a rigid body. The particles that constitute the wheel do experience a centripetal acceleration directed towards the center. This acceleration arises due to internal elastic force which cancels out in pairs.

Step 2: Interpret the motion of half wheel.

In a half wheel, the distribution of mass about its centre of mass (through which axis of rotation passes) is not symmetrical. Therefore, the direction of the angular momentum of the wheel does not coincide with the direction of its angular velocity. Hence, an external torque is required to maintain the motion of the half wheel.

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