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


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

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Chapter 7: System of Particles and Rotational Motion - Exercises [Page 180]


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


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