Before You Begin

Question #42392

Difficulty: 8/10 | 🟢 Free

The Question

A uniform solid disk of mass $m$ and radius $R$ is initially rolling without slipping on a rough horizontal surface with a constant velocity $v_0$ . An impulsive force of magnitude $J$ is applied at the center of mass of the disk. The impulse is directed downwards at an angle of $60^\circ$ below the horizontal, and its horizontal component is opposite to the direction of $v_0$ . The coefficient of kinetic friction between the disk and the surface is $\mu = \frac{1}{6\sqrt{3}}$ . What is the angular velocity of the disk immediately after the impulse? (Assume clockwise rotation is positive)

Options

A.
$\frac{v_0}{R} - \frac{J}{6mR}$
B.
$\frac{v_0}{R} - \frac{J}{3mR}$
C.
$\frac{v_0}{R}$
D.
$\frac{v_0}{R} + \frac{J}{6mR}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Impulsive Torque and Angular Momentum|Torque about non-fixed axes|Change in Velocity (Δv)

Why This Question Is Tricky

Common Mistakes

This question tests the transition from rolling to sliding under an impulsive force.

Students often incorrectly assume that the point of contact remains an instantaneous axis of rotation (IAOR) during the impulse, leading them to apply angular momentum conservation about the contact point and enforce the rolling constraint ( $v = \omega R$ ).

This ignores the fact that the required friction to maintain rolling exceeds the maximum available impulsive friction ( $\mu N_{imp}$ ), causing the disk to slip.

Consequently, the angular impulse must be evaluated about the center of mass using the kinetic friction impulse.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	System of Particles and Rotational Motion - Class 11 Part 1
Concept	Impulsive Torque and Angular Momentum
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free