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Question #42371
The Question
A uniform solid cylinder of mass and radius rests on a rough horizontal surface with a coefficient of friction . A sharp impulse of magnitude is applied to the cylinder at its topmost point. The line of action of the impulse is directed downwards at an angle below the horizontal. What is the angular velocity of the cylinder immediately after the impulse?
Options
- A.
- B.
- C.
- D.
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Multi-Concept_Bridge
Master problems that require linking physics and math concepts to solve complex competitive questions.
Concepts Behind This Question
Rigid Body Constraints|Impulse-Momentum Theorem|FBD Isolation
Why This Question Is Tricky
Common Mistakes
This question tests the student's ability to handle impulsive constraints and the instantaneous transition from static to kinetic friction during an impact.
A common trap is assuming that impulsive friction is zero because normal forces are typically non-impulsive.
However, the downward component of the applied impulse generates an impulsive normal force, activating impulsive friction.
Students must first test the pure rolling hypothesis to find the required friction, compare it against the limiting impulsive friction , and correctly apply the kinetic impulsive friction in the proper direction (forwards, opposing the backward slip of the contact point) to find the true angular velocity.
Failing to check the pure rolling condition leads to the incorrect assumption of static friction, while ignoring impulsive friction entirely leads to a standard, but incorrect, rigid body result.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | System of Particles and Rotational Motion - Class 11 Part 1 |
| Concept | Rigid Body Constraints |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |