A disc rotating about its axis with angular speed ω₀ is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in Fig. 7.41? Will the disc roll in the direction indicated?

Question

Philoid · Accepted Answer

Velocity of a point on a rolling disc is given by,

'V= dω'

Where,

d = Distance from center of rotation

ω = Angular velocity of the body

Now, Velocity at points A and B are same and equal to Rω₀

(∵ distance between points A& B and centre of rotation = R)

⇒ v_A = v_B = Rw₀

Now,

Velocity at point C,

(∵ distance between point C and centre of rotation = )

No, Disc will rotate in the shown direction below.