Angular Displacement, Angular Velocity and Angular Acceleration
Physics · System Of Particles And Rotational Motion · NEET
When a rigid body rotates, every particle turns through the same angle. That turned angle is the angular displacement (θ, in radians); how fast θ changes is the angular velocity ω = dθ/dt (rad/s); how fast ω changes is the angular acceleration α = dω/dt (rad/s²). Memory hook: they are the exact rotation copies of s, v and a in straight-line motion, so θ→ω→α behaves just like s→v→a.
Left: all points of a spinning disc share one ω, but linear speed v = ωr grows with distance r from the axis. Right: ω and α are axial vectors pointing along the rotation axis (right-hand rule), not radial or tangential.
Your doubts, answered
Is angular displacement in degrees or radians? Which do I use in NEET formulas?
Always use radians in NEET formulas. All rotational equations (ω = θ/t, v = ωr, α = ω/t) assume θ is in radians. Convert first: 1 revolution = 2π rad = 360°, so degrees × (π/180) = radians. A common slip is plugging in degrees or revolutions directly and getting a wrong number.
Why do all particles of a rotating body have the SAME angular velocity but DIFFERENT linear velocity?
In pure rotation every particle sweeps the same angle in the same time, so ω is identical for the whole body. But linear speed is v = ωr, so a particle farther from the axis (larger r) moves faster. This is why the rim of a disc moves faster than a point near its centre, even though ω is one single value for the disc.
Is angular velocity a scalar or a vector, and where does it point?
Angular velocity is a vector (an axial vector). It points ALONG the axis of rotation, not along the radius and not along the tangent. Use the right-hand rule: curl the fingers of your right hand in the direction of rotation, and the thumb points along ω. NEET tests this exact direction fact.
How do I convert rpm to rad/s quickly?
Multiply rpm by 2π/60. Reason: 1 revolution = 2π rad and 1 minute = 60 s, so ω (rad/s) = N (rpm) × 2π/60 = N × π/30. Example: 300 rpm = 300 × π/30 = 10π rad/s. NEET PYQs almost always give speed in rpm to check if you convert.
What is the difference between angular velocity and angular acceleration?
Angular velocity ω tells how fast the body is turning right now (rad/s). Angular acceleration α tells how fast that turning rate is changing (rad/s²). If ω is constant, α = 0 even though the body keeps rotating. α = dω/dt = Δω/Δt for uniform change.
⚠️ The NEET trap ✗ Angular acceleration of a body moving in a circle points along the tangent (or toward the centre). ✓ Angular velocity ω and angular acceleration α are axial vectors — they point ALONG the axis of rotation (right-hand rule), never along the radius or tangent. The tangential/centripetal directions belong to LINEAR acceleration, not to α. 🧠 Radial and tangential are linear-motion directions; angular vectors always live on the axle.
Real NEET questions
NEET 2022
A flywheel's angular speed changes uniformly from 1200 rpm to 3120 rpm in 16 s. Its angular acceleration (rad/s²) is:
A flywheel's angular speed increases uniformly from 600 rpm to 1200 rpm in 10 s. The number of revolutions completed in this time is:
A · 900
B · 600
C · 150 ✓
D · 300
Solution: Step 1 — work in rev/s (keep counting revolutions). n0 = 600/60 = 10 rev/s, n = 1200/60 = 20 rev/s. Step 2 — the change is uniform, so use the rotational analogue of average speed: revolutions = (average rate) × time = ((n0 + n)/2) × t. Step 3 — revolutions = ((10 + 20)/2) × 10 = 15 × 10 = 150. Answer: C. (Same idea as s = ((u+v)/2)t in straight-line motion.)
NEET 2023
The angular acceleration of a body moving along the circumference of a circle is directed:
A · along the radius, away from the centre
B · along the radius, towards the centre
C · along the tangent to its position
D · along the axis of rotation ✓
Solution: Angular velocity ω and angular acceleration α are axial vectors. By the right-hand rule they lie ALONG the axis of rotation, perpendicular to the plane of the circle — not radial and not tangential. Radial (centre-pointing) and tangential directions describe LINEAR acceleration, not angular acceleration. Answer: D.
Solved System Of Particles And Rotational Motion NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What are the SI units of angular displacement, angular velocity and angular acceleration?
Angular displacement θ is in radian (rad, dimensionless). Angular velocity ω is in rad/s. Angular acceleration α is in rad/s². Radian has no dimension, so ω has dimension [T⁻¹] and α has [T⁻²].
What is the formula linking angular velocity and linear velocity?
v = ωr, where v is the linear (tangential) speed of a particle, ω is the angular velocity of the body, and r is the distance of that particle from the axis. This is why outer particles move faster.
Are there rotational equations of motion like v = u + at?
Yes. For constant α: ω = ω0 + αt, θ = ω0 t + (1/2)αt², and ω² = ω0² + 2αθ. They are exact copies of the straight-line equations with s→θ, u→ω0, v→ω, a→α.
Is angular velocity same as frequency?
They are related but not equal. ω = 2πf, where f is frequency in rev/s (Hz). So a body spinning at f = 5 rev/s has ω = 10π rad/s. Always convert rpm/frequency to rad/s before using rotational formulas.
Can angular displacement be treated as a vector?
Large angular displacements do NOT add like vectors (order matters), so finite θ is not a true vector. But very small (infinitesimal) angular displacements dθ, and hence ω and α, ARE vectors directed along the axis of rotation.
