Physics · System Of Particles And Rotational Motion · NEET
Yes. NCERT builds them the same way. You just change the symbols. Linear s, u, v, a become angular θ, ω₀, ω, α. So v = u + at becomes ω = ω₀ + αt; s = ut + ½at² becomes θ = ω₀t + ½αt²; and v² = u² + 2as becomes ω² = ω₀² + 2αθ. If you already know the linear set, you know the angular set. This is why NEET expects you to solve rotation problems as fast as straight-line problems.
One full rotation is 2π radians, and one minute is 60 seconds. So ω (rad/s) = rpm × 2π / 60 = rpm × π/30. Example: 1200 rpm = 1200 × π/30 = 40π rad/s. Almost every NEET flywheel question gives you rpm, so do this conversion first, before touching any equation. Forgetting it is the single most common mistake.
Only when the angular acceleration α is constant (uniform). If α changes with time, these equations do not apply and you must use calculus. In NEET, words like 'uniformly', 'constant angular acceleration', or 'changes uniformly' are your green signal to use them. A flywheel speeding up uniformly qualifies; a body with time-varying torque may not.
Angular acceleration α measures how fast the spin rate ω changes and is measured in rad/s². Tangential acceleration a_t is the linear acceleration of a point on the rim along its path, measured in m/s². They are linked by a_t = rα, where r is the distance from the axis. So α is the same for the whole rigid body, but a_t is larger for points farther from the axis.
First find the total angle θ turned (in radians) using θ = ω₀t + ½αt², or use the average: θ = (ω₀ + ω)/2 × t. Then divide by 2π to get revolutions, because one revolution = 2π radians. Number of revolutions n = θ / (2π). If everything is already in rpm and minutes, you can even count revolutions directly using average rpm × time.
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 particle starts from rest and moves in a circle of radius r, attaining speed V₀ in the n-th round. Its angular acceleration is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
ω = ω₀ + αt, θ = ω₀t + ½αt², and ω² = ω₀² + 2αθ. Here ω₀ is initial angular velocity, ω is final angular velocity, α is angular acceleration, θ is angle turned, and t is time. They mirror the linear v = u + at set exactly.
Angle θ is in radian (rad), angular velocity ω in rad/s, angular acceleration α in rad/s², and time t in seconds. Always convert rpm and degrees to radians and seconds before solving.
No. These equations hold only for constant (uniform) angular acceleration. If α varies with time, you must integrate. NEET problems signal constant α with words like 'uniformly' or 'constant angular acceleration'.
By the rotational form of Newton's second law, torque τ = Iα, where I is the moment of inertia. So a constant torque gives a constant α, which then lets you use these kinematics equations. This is the bridge to the next topic, dynamics of rotation.
Every year NEET asks 1–2 direct questions on flywheels, discs, or particles speeding up or slowing down on a circle. They are quick, formula-based marks if you convert rpm correctly and pick the right of the three equations.
