An annular disk of mass 𝑀, inner radius 𝑎 and outer radius 𝑏 is placed on a horizontal surface with
coefficient of friction 𝜇, as shown in the figure. At some time, an impulse ℐ0𝑥̂ is applied at a height
ℎ above the center of the disk. If ℎ = ℎ𝑚 then the disk rolls without slipping along the 𝑥-axis.
Which of the following statement(s) is(are) correct?
(A) For 𝜇 ≠ 0 and 𝑎 → 0, ℎ𝑚 = 𝑏/2.
(B) For 𝜇 ≠ 0 and 𝑎 → 𝑏, ℎ𝑚 = 𝑏.
(C) For ℎ = ℎ𝑚, the initial angular velocity does not depend on the inner radius 𝑎.
(D) For 𝜇 = 0 and ℎ = 0, the wheel always slides without rolling.
In this video, we solve an advanced rotational motion problem involving an annular disk that is given an impulse at a specific height. This leads to conditions for rolling without slipping along the x-axis. We derive the relationship between height, friction, and the radius for rolling motion and analyze how the angular velocity is affected."
🌀 What You'll Learn:
The conditions for an annular disk to roll without slipping after receiving an impulse.
Application of rotational dynamics, moment of inertia, and frictional forces to analyze the system.
Step-by-step approach to determine angular velocity, sliding conditions, and height relations for complex systems.
✨ Benefits You'll Gain:
Perfect for JEE aspirants aiming to deepen their understanding of rotational motion and conditions for rolling without slipping.
Learn how to apply Newton's laws to analyze forces, torques, and energy in rotational systems.
Master problem-solving techniques for tackling advanced questions on rolling and rotational kinematics.
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24 окт 2024
