A disc rotating about its axis with angular speed ω_ois 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?

Solution

Angular speed of the disc = ω_o

Radius of the disc = R

Using the relation for linear velocity, v = ω_oR

For point A:
v_A = Rω_o,in the direction tangential to the right.
For point B:
v_B = Rω_o, in the direction tangential to the left.
For point C:
v_c =

open parentheses straight R over 2 close parentheses

ω_o,in the direction same as that of v_{_A.}

v_A = Rω_o;
v_B = Rω₀,
v_c =

open parentheses straight R over 2 close parentheses

ω₀

_{The disc will not roll.}
The directions of motion of points A, B, and C on the disc are shown in the following figure

Since the disc is placed on a frictionless table, it will not roll. This is because the presence of friction is essential for the rolling of a body.

Some More Questions From Units and Measurement Chapter

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Units And Measurement

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