Centre of mass, torque, angular momentum, moment of inertia, rolling motion.
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Q1 · System of Particles and Rotational Motion · MEDIUM
A uniform rod of length L and mass M is pivoted at one end and can rotate freely in a vertical plane. It is released from rest in a horizontal position. What is the angular velocity of the rod when it becomes vertical?
Q2 · System of Particles and Rotational Motion · MEDIUM
A uniform rod of length L and mass M is pivoted at one end and can rotate freely in a vertical plane. The rod is released from the horizontal position. What is the angular acceleration of the rod at the instant of release? (Take g as acceleration due to gravity)
Q3 · System of Particles and Rotational Motion · MEDIUM
A uniform solid sphere and a uniform hollow sphere of the same mass and radius are released from rest at the top of an inclined plane. Both roll without slipping. Which statement is correct?
Q4 · System of Particles and Rotational Motion · MEDIUM
A uniform disc of mass M and radius R is rotating about its central axis with angular velocity ω₀. A small particle of mass m drops vertically onto the edge of the disc and sticks to it. What is the new angular velocity of the system?
Q5 · System of Particles and Rotational Motion · EASY
A uniform disc of mass 2 kg and radius 0.5 m is rotating about an axis passing through its center and perpendicular to its plane with an angular velocity of 10 rad/s. What is the rotational kinetic energy of the disc?