First slide

Rolling motion

Question

In pure rolling motion of a ring
a) it rotates about instantaneous point of contact of ring and ground
b) its centre of mass moves in translatory motion only
c) its centre of mass will have translatory as well as rotatory motion

Moderate

A

only a is correct
B

a and c are correct
C

a and b are correct
D

a, b and c are correct

Solution

In the diagram shown, O is the point of contact of the ring with the surface. So point O is on surface as well as on the ring. In case of pure rolling, the ring does not slip on the surface. Since the surface is stationary, velocity of point O is called instantaneous centre of rotation and at the instant shown in figure, the entire ring rotates with angular velocity $ω$ = V/R about point O.
The distance of COM c from the surface always remains R. So COM moves in translatory motion only. Hence, (a) and (b) are correct.

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