# A Disc Rotating About Its Axis with Angular Speed ωo is Placed Lightly (Without Any Translational Push) on a Perfectly Frictionless Table What Are the Linear Velocities of the Points A, B and C on the Disc Shown in Figure? Will the Disc Roll in the Direction Indicated - Physics

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A disc rotating about its axis with angular speed ωois 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 Figure? Will the disc roll in the direction indicated?

#### Solution 1

vA = RωovB = Rωo;  v_c = (R/2)omega_o

The disc will not roll Angular speed of the disc = ωo

Radius of the disc = R

Using the relation for linear velocity, v = ωoR

For point A:

vA = Rωo; in the direction tangential to the right

For point B:

vB = Rωo; in the direction tangential to the left

For point C:

v_c = (R/2)omega_o in the direction same as that of vA

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.

#### Solution 2

Since v = romega

For Point A, v_A = Romega_0 in the direction of arrow

For point B, v_B = Romega_0 in the opposite direction of arrow

For point C, v_C = R/2omega_0 in  the direction of arrow

The disc will not roll in the given direction because friction is necessary for the same

Is there an error in this question or solution?
Chapter 7: System of Particles and Rotational Motion - Exercises [Page 180]

#### APPEARS IN

NCERT Physics Class 11
Chapter 7 System of Particles and Rotational Motion
Exercises | Q 28 | Page 180
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