A uniform rod of length $L$, mass $M$ is hinged at one end and free to swing in a vertical plane. The maximum angular velocity (when rod swings to vertical) starting from horizontal:
Two discs of MI $I_1$ and $I_2$ rotating with $\omega_1$ and $\omega_2$ are brought into contact face to face along their axes. The common angular velocity:
A circular disc rolls without slipping. The ratio of translational KE to rotational KE:
A solid sphere of $M, R$ rolls without slipping on a horizontal surface, hits a step of height $R/4$. Minimum $v$ to climb step ($g$ = gravity):
A solid sphere is initially at rest on a rough horizontal surface. A horizontal impulse is applied at height $h$ above the centre. For the sphere to undergo pure rolling without slipping, $h$ should be:
A particle moves in a circle. Its angular momentum about the centre changes if:
A wheel of moment of inertia $I$ and radius $r$ has been mounted on a horizontal axle. A string is wound on it and a mass $m$ hangs from it. The angular acceleration:
A flywheel of mass $5$ kg, radius $0.2$ m rotates at $40$ rad/s. Power developed to keep it rotating against friction torque of $0.2$ N·m:
The angular momentum about origin of a particle of mass $1$ kg at $(2, 3, 0)$ m moving with velocity $(4, 0, 0)$ m/s is:
The MI of a uniform rectangular plate of mass $M$, sides $a$ and $b$ about a perpendicular axis through its centre is:
A solid sphere of mass $2$ kg, radius $0.1$ m rotates at $20$ rad/s. Its rotational KE (J):
A wheel of $I = 0.5$ kg·m² accelerates from rest at $4$ rad/s². Number of revolutions in $5$ s (rounded):
A ring of radius $0.5$ m, mass $2$ kg rolls without slipping at $2$ m/s. Total KE (J):
Assertion (A): A spinning skater rotates faster when she pulls in her arms. Reason (R): Her angular momentum increases.
Assertion (A): For a body rolling without slipping, kinetic friction does no work. Reason (R): The contact point of the rolling body is instantaneously at rest, so kinetic friction does no displacement.
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