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Foundation3 past questions

Rotational kinematics and dynamics

Rotational kinematics describes the motion of rotating bodies, while dynamics relates torque, angular acceleration, and rotational kinetic energy.

Why this shows up in the exam

You must connect angular velocity, acceleration, torque, and energy to solve NEET problems on rotating systems.

How NEET tests this

Numerical · 2 QsApplicationStatement analysis

Learn the idea

Rotational kinematics links angular displacement, velocity and acceleration; dynamics ties torque to angular acceleration and power to torque×angular speed – the key is the single formula P=τω.

🧠 Memory hook: Power = Torque × Speed – like a cyclist: harder push (torque) or faster pedalling (ω) gives more power; remember the ‘T×S’ shortcut.

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • Power P (W) = torque τ (Nm) × angular speed ω (rad s⁻¹)
  • Angular speed ω = 2π N/60 where N is rev min⁻¹
  • Torque τ = I α where I is moment of inertia and α angular acceleration
  • Rotational kinetic energy K = ½ I ω²
  • For a solid disc I = ½ M R²
  • Units must be consistent: kW → W, rev min⁻¹ → rad s⁻¹

How to approach it

  1. 1Convert the given rev min⁻¹ to rad s⁻¹ using ω=2πN/60
  2. 2Write the power relation P=τω and substitute the known P and ω
  3. 3Solve for τ = P/ω
  4. 4Check the answer’s unit (Nm) and round appropriately

Worked example — watch it click

An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver?

  • A)350 Nm
  • B)440 Nm
  • ✅531 Nm
  • D)628 Nm

The concept behind this problem

The worked example forces you to translate a rotational speed given in rev min⁻¹ into angular speed and then apply the fundamental power‑torque relation, a staple of rotational dynamics.

Step by step

  1. 1Power P = τω, where τ is torque and ω is angular velocity.
  2. 2P = 100 kW = 100000 W. ω = 1800 rev/min = 1800×2π/60 = 60π rad/s = 188.5 rad/s. τ = P/ω = 100000/188.5 = 530.5 ≈ 531 Nm.

Watch out

Students often treat 1800 rev min⁻¹ as 1800 rad s⁻¹, which yields a torque about 55 Nm – far from the correct 531 Nm.

Common slip-ups that cost marks

  • •Using rev min⁻¹ directly as ω (forgetting the 2π/60 factor)
  • •Mixing kW with W without conversion
  • •Confusing linear speed V with angular speed ω when the problem involves a rolling wheel

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 3

An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver?

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