Moment of inertia, torque, angular momentum, rolling motion, banking of road.
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Q1 · Rotational Dynamics (Class 12) · MEDIUM
A solid sphere of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal surface with a linear velocity of 4 m/s. What is the total kinetic energy of the sphere? (Moment of inertia of solid sphere about its diameter = (2/5)MR²)
Q2 · Rotational Dynamics (Class 12) · EASY
A disc of mass 4 kg and radius 0.2 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 angular momentum of the disc? (Moment of inertia of disc about its center = (1/2)MR²)
Q3 · Rotational Dynamics (Class 12) · MEDIUM
A car of mass 1000 kg is moving on a circular road of radius 50 m banked at an angle θ such that tan θ = 0.5. What is the optimum speed at which the car can take the turn without friction? (Take g = 10 m/s²)
Q4 · Rotational Dynamics (Class 12) · MEDIUM
A disc of radius 0.2 m and mass 2 kg is rotating about its central axis with angular velocity 10 rad/s. What is the angular momentum of the disc?