Torque, angular momentum, moment of inertia, rolling motion.
Test yourself on Rotational Mechanics
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Q1 · Rotational Mechanics · HARD
A uniform solid cylinder of mass M and radius R rolls without slipping down a rough inclined plane of inclination 30°. A light thread wound around the cylinder passes over a frictionless pulley and is attached to a block of mass m = M/3 hanging vertically. The acceleration of the center of mass of the cylinder is (g = 10 m/s²):
Q2 · Rotational Mechanics · HARD
A uniform rod of length L and mass M is pivoted at one end and released from horizontal position. When it reaches the vertical position, the angular velocity ω and the hinge reaction R at the pivot are respectively:
Q3 · Rotational Mechanics · HARD
A uniform solid cylinder of mass M and radius R is set into rotation about its axis with angular velocity ω₀. It is then placed on a rough horizontal surface (coefficient of friction μ). The time taken for pure rolling to begin is:
Q4 · Rotational Mechanics · HARD
A uniform solid cylinder of mass M and radius R rolls without slipping down an inclined plane from rest. If the incline makes an angle θ with the horizontal and has length L, the angular momentum of the cylinder about the point of contact when it reaches the bottom is:
Q5 · Rotational Mechanics · HARD
A uniform solid cylinder of mass M and radius R rolls without slipping down a rough inclined plane. The ratio of its rotational kinetic energy to its total kinetic energy at any instant is: