Rotational Motion of a Rigid Body: Moment of Inertia
ICSE · Class 11 · Physics
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Explore the full setState the definition of torque and write its vector formula.
Answer
Torque is the moment of a force about an axis or point. Formula: τ = r × F. Magnitude: τ = rF sinθ. It is a vector quantity. Unit: N-m.
A force of 10 N is applied perpendicular to a door at a distance of 0.5 m from the hinge. Find the torque.
Answer
Given: F = 10 N, r = 0.5 m, θ = 90° Formula: τ = rF sinθ Step 1: τ = (0.5 m)(10 N)sin90° Step 2: τ = (0.5)(10)(1) N-m Step 3: τ = 5 N-m Answer: 5 N-m…
Why is torque maximum when force is applied perpendicular to the position vector?
Answer
Because τ = rF sinθ and sin90° = 1. Only the transverse component of force contributes to torque, so a right-angle push produces the greatest turning effect. A door opens most easily when pushed at it…
A force is applied at the hinge line of a door. Why does it not produce rotation?
Answer
At the hinge line, r = 0. Since τ = r × F, torque becomes zero. So even a large force cannot produce rotation if the lever arm is zero.
State the difference between work and torque.
Answer
Work is scalar and torque is vector. Both have the same dimensions [ML²T⁻²] and both can be written in N-m, but work is measured as joule while torque is measured as newton-metre.
A force of 20 N acts on a point 3 m from the axis at an angle of 30° with the position vector. Find the torque.
Answer
Given: F = 20 N, r = 3 m, θ = 30° Formula: τ = rF sinθ Step 1: τ = (3 m)(20 N)sin30° Step 2: τ = 60 × 1/2 N-m Step 3: τ = 30 N-m Answer: 30 N-m…
State the definition of angular momentum and write its vector formula.
Answer
Angular momentum is the moment of linear momentum about an axis. Formula: L = r × p. Magnitude: L = rp sinθ. Unit: kg-m²-s⁻¹ or J-s.
A particle has linear momentum 6 kg-m/s and is 2 m from the axis with momentum perpendicular to r. Find angular momentum.
Answer
Given: p = 6 kg-m/s, r = 2 m, θ = 90° Formula: L = rp sinθ Step 1: L = (2 m)(6 kg-m/s)sin90° Step 2: L = 12 kg-m²-s⁻¹ Answer: 12 kg-m²-s⁻¹…
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