Rotational and Circular Motion

Rotational and Circular Motion deals with bodies that rotate about an axis or move along curved paths. The PMDC MDCAT 2026 syllabus keeps this chapter deliberately narrow: angular displacement, angular velocity, and the conversions between angular and linear quantities. Unit conversions and v = rω are the perennial MCQ favourites.

PMC Table of Specifications. Three subtopics only — Angular Displacement (including revolution, degree and radian), Angular Velocity, and the Relation between Angular & Linear Quantities (displacement, velocity, acceleration).

Angular Displacement

Angular displacement θ is the angle (in radians) swept out by a rotating radius vector. SI unit: radian (rad). It is dimensionless but treated as a vector along the axis of rotation (right-hand rule).

For a particle traversing arc length s on a circle of radius r:

θ = s/r (radians)

Useful conversions:

1 revolution = 2π rad = 360°.
1 rad = 180°/π ≈ 57.3°.
π/2 rad = 90°; π rad = 180°.

Angular Velocity

Angular velocity ω is the rate of change of angular displacement:

ω = Δθ/Δt (instantaneous: ω = dθ/dt)

SI unit: rad/s. Direction is along the axis of rotation by the right-hand rule. Closely related quantities:

Time period T: Time for one revolution: T = 2π/ω.
Frequency f: Number of revolutions per second: f = 1/T = ω/(2π). SI unit: hertz (Hz).
Angular acceleration α: Rate of change of angular velocity: α = dω/dt. SI unit: rad/s².

Relation between Angular and Linear Quantities

For a particle at radius r from the rotation axis, the angular and linear quantities are connected by:

Linear vs Angular quantities — the syllabus relations
Quantity	Linear	Angular	Relation
Displacement	s (m)	θ (rad)	s = rθ
Velocity	v (m/s)	ω (rad/s)	v = rω
Acceleration	a (m/s²)	α (rad/s²)	a_t = rα (tangential)
Acceleration (curved)	a_c (m/s²)	—	a_c = v²/r = rω² (centripetal)

Memory aid. "Multiply by r to go from angular to linear." s = rθ, v = rω, a_t = rα. Then for centripetal a_c = v²/r — the only one that divides by r.

Common trap. In uniform circular motion the speed is constant but the velocity is not — its direction is constantly changing. Hence there is acceleration (centripetal, directed toward the centre) even when speed is unchanged.

Worked MCQs

Five MCQs that capture the high-yield testing patterns for this chapter.

Q1. An angle of 60° in radians is:

π/2
π/4
π/3
π/6

Convert: 60° × (π/180) = π/3 rad.

Q2. A wheel rotates at 300 rpm. Its angular velocity in rad/s is:

5
10π
20π
300

300 rpm = 5 rev/s. ω = 2πf = 2π × 5 = 10π rad/s.

Q3. The linear speed of a point on the rim of a disc of radius 0.2 m rotating at 50 rad/s is:

2.5 m/s
5 m/s
10 m/s
250 m/s

v = rω = 0.2 × 50 = 10 m/s.

Q4. A particle moves along a circle of radius 0.50 m and sweeps out an angular displacement of 2.0 rad. The arc length covered is:

0.25 m
1.0 m
2.5 m
4.0 m

s = rθ = 0.50 × 2.0 = 1.0 m. The angle must be in radians — that is exactly why θ = s/r is defined the way it is.

Q5. In uniform circular motion:

Speed and velocity are both constant
Speed and velocity are both variable
Speed is constant but velocity changes
Velocity is constant but speed changes

Magnitude (speed) is unchanged, but direction of motion is constantly changing — therefore velocity changes and there is centripetal acceleration.

Quick Recap

1 rev = 2π rad = 360°.
ω = dθ/dt; T = 2π/ω; f = 1/T.
v = rω, a_t = rα, a_c = v²/r = rω².
θ = s/r; multiply by r to convert angular → linear.
Speed constant, velocity changes → centripetal acceleration exists.

Test yourself. Take a timed Circular Motion quiz or browse all Physics MCQs to lock these concepts in.