System of Particles & Rotational Motion

A wheel starts from rest and is given a uniform angular acceleration of 4 rad/s². What is its angular velocity after 5 seconds?

A disc rotates at a constant angular velocity of 10 rad/s. What angular displacement does it cover in 6 seconds?

A point on a rotating body is at a distance of 0.5 m from the axis. If the body's angular velocity is 8 rad/s, what is the linear speed of that point?

A particle of mass 2 kg is located 0.5 m from an axis of rotation. What is its moment of inertia about that axis?

A disc of mass 2 kg and radius 0.2 m has its moment of inertia I_CM about an axis through its centre, perpendicular to its plane. Using the parallel axis theorem, find its moment of inertia about a parallel axis 0.3 m away from the centre.

The moment of inertia of a uniform disc about one of its diameters is 0.5 kg·m². Using the perpendicular axis theorem, find its moment of inertia about an axis through its centre, perpendicular to its plane.

A uniform rod of mass 3 kg and length 2 m rotates about a perpendicular axis through its centre. Find its radius of gyration about this axis.

A force of 10 N is applied at a point 0.4 m from a pivot, making an angle of 30° with the rod. Find the magnitude of the torque produced about the pivot.

A wheel has a moment of inertia of 4 kg·m² about its axis. What torque is needed to give it an angular acceleration of 3 rad/s²?

A cyclist goes around a horizontal circular turn of radius 20 m at a speed of 10 m/s. Taking g = 10 m/s², at what angle to the vertical must the cyclist lean?

A particle of mass 0.5 kg moves with a speed of 4 m/s along a straight line. The perpendicular distance from a fixed point O to this line is 2 m. What is the particle's angular momentum about O?

A rigid body has a moment of inertia of 2 kg·m² and is spinning at 5 rad/s. Find its angular momentum.

A skater spinning with moment of inertia 5 kg·m² at 2 rad/s pulls her arms in, reducing her moment of inertia to 2 kg·m². No external torque acts on her. Find her new angular velocity.

An ice skater pulls in her arms while spinning freely, reducing her moment of inertia. Which statement about her angular momentum (L) and rotational kinetic energy (KE_rot) is correct?

A flywheel has a moment of inertia of 4 kg·m² and spins at 6 rad/s. Find its rotational kinetic energy.

A wheel of radius 0.5 m rolls on the ground without slipping with its centre moving at 10 m/s. Find its angular velocity.

A solid sphere of mass 2 kg rolls without slipping with a centre-of-mass speed of 4 m/s. Find its total kinetic energy. (For a solid sphere, K²/R² = 2/5.)

A solid sphere rolls down a rough incline, without slipping, starting from rest at a height of 7 m. Taking g = 10 m/s², find its speed at the bottom. (For a solid sphere, K²/R² = 2/5.)