Rotational Motion – Stage 2 (Page 4)

Board Exam Numerical Problems (Step-wise Solutions)

This section contains important numerical problems frequently asked in Board examinations. Each problem is solved in a clear, exam-friendly manner.

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Problem 1

A solid disc of mass 2 kg and radius 0.5 m rotates with angular velocity 10 rad s⁻¹. Find its rotational kinetic energy.

Given:
Mass, M = 2 kg
Radius, R = 0.5 m
Angular velocity, ω = 10 rad s⁻¹

Formula:
Moment of inertia of solid disc, I = ½ MR²

I = ½ × 2 × (0.5)² = 0.25 kg m²

Rotational kinetic energy:

K = ½ Iω² = ½ × 0.25 × 10² = 12.5 J

Answer: Rotational kinetic energy = 12.5 J

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Problem 2

Find the moment of inertia of a uniform rod of mass 3 kg and length 2 m about an axis passing through its center and perpendicular to its length.

Given:
Mass, M = 3 kg
Length, L = 2 m

Formula:

I = ML² / 12

I = 3 × (2)² / 12 = 1 kg m²

Answer: Moment of inertia = 1 kg m²

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Problem 3

A wheel starts from rest and attains an angular velocity of 20 rad s⁻¹ in 4 seconds. Find its angular acceleration.

Given:
Initial angular velocity, ω₀ = 0
Final angular velocity, ω = 20 rad s⁻¹
Time, t = 4 s

Formula:

α = (ω − ω₀) / t

α = (20 − 0) / 4 = 5 rad s⁻²

Answer: Angular acceleration = 5 rad s⁻²

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Problem 4

A disc rolls without slipping with a velocity of 4 m s⁻¹. Find its angular velocity if radius is 0.2 m.

Given:
Linear velocity, v = 4 m s⁻¹
Radius, R = 0.2 m

Formula (pure rolling):

v = ωR

ω = v / R = 4 / 0.2 = 20 rad s⁻¹

Answer: Angular velocity = 20 rad s⁻¹

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Problem 5

A torque of 10 N m acts on a wheel having moment of inertia 2 kg m². Find its angular acceleration.

Given:
Torque, τ = 10 N m
Moment of inertia, I = 2 kg m²

Formula:

τ = Iα

α = τ / I = 10 / 2 = 5 rad s⁻²

Answer: Angular acceleration = 5 rad s⁻²

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Board Exam Tip

✔ Always write units
✔ Box the final answer
✔ Do not skip steps
✔ Use correct formula for correct body

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Next: Stage 2 – Page 5
Mixed Concept Numericals & Common Mistakes

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