Rotational Motion of a Rigid Body: Moment of Inertia — Practice Quiz
ICSE · Class 11 · Physics
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Quick Quiz: Rotational Motion of a Rigid Body: Moment of Inertia
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A wheel starts from rest and has a constant angular acceleration of 3.0 rad/s². If it rotates for 4.0 s, what is its angular velocity at the end of 4.0 s?
A body starts from rest with constant angular acceleration 2.5 rad/s². How much angular displacement does it cover in 6.0 s?
A disc of moment of inertia 8.0 kg m² is acted upon by a torque of 20 N m. What is its angular acceleration?
A rotating body has angular momentum 18 kg m²/s and moment of inertia 3.0 kg m². What is its angular velocity?
Sample Questions
A body has angular momentum 24 kg m²/s and moment of inertia 8.0 kg m². If the angular momentum remains constant and the moment of inertia becomes 6.0 kg m², what is the new angular velocity?
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4.0 rad/s
Since L = Iω remains constant, first confirm L = 24 kg m²/s. For the new situation, ω = L/I = 24/6.0 = 4.0 rad/s.
A ring of mass 4.0 kg and radius 0.50 m rotates about its central axis perpendicular to its plane with angular velocity 10 rad/s. What is its rotational kinetic energy?
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50 J
For a ring about its central axis, I = MR² = 4.0 × 0.50² = 4.0 × 0.25 = 1.0 kg m². Then K = 1/2 Iω² = 1/2 × 1.0 × 10² = 50 J.
A rigid body has moment of inertia 9.0 kg m² and rotational kinetic energy 72 J. What is its angular velocity?
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4.0 rad/s
Use K = 1/2 Iω². So 72 = 1/2 × 9.0 × ω² = 4.5ω². Hence ω² = 16 and ω = 4.0 rad/s.
A body with angular momentum 30 kg m²/s has its moment of inertia reduced from 10 kg m² to 6.0 kg m² without external torque. What is the ratio of the final angular velocity to the initial angular velocity?
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5/3
With no external torque, Iω is constant. So I₁ω₁ = I₂ω₂. Therefore ω₂/ω₁ = I₁/I₂ = 10/6 = 5/3.
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