Rotational Kinetic Energy and Power
For fixed-axis rigid rotation, rotational kinetic energy is K = one half I omega squared, and instantaneous power delivered by a torque is the scalar product tau dot omega.
Why this shows up in the exam
Flywheel energy storage · Comparing rotating bodies · Motor power and spin-up calculations
Learn the idea
A rigid body's spin energy is one half its inertia times angular speed squared. A rigid body's spin energy is one half its inertia times angular speed squared. Start from a clear axis, origin, body, and reference frame; the geometry and constraints then decide which rotational law is safe to use.
🧠 Memory hook: Spin energy uses omega squared; power uses torque times omega.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- K_rot = (1/2) I omega² — Rotational kinetic energy about the spin axis.
- P = tau dot omega — Instantaneous rotational power.
- W = integral tau dtheta — Work done by torque through angular displacement.
How to approach it
- 1Identify the rotation axis and inertia
- 2Separate rotational from translational energy
- 3Use work or power with consistent angular units
Common slip-ups that cost marks
- •Using mass instead of moment of inertia
- •Omitting translational energy of a rolling body
- •Using final torque times angle when torque varies
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Masses 1 kg and 3 kg lie at x = 0 and x = 4 m. Find the x-coordinate of their centre of mass.
More from Motion of System of Particles and Rigid Body
Conservation of momentum and angular momentum
The total linear and angular momentum of a system remains constant in the absence of external forces or torques, including during collisions and rotational motion.
Moment of inertia and radius of gyration
Moment of inertia quantifies how mass is distributed with respect to an axis of rotation, and the radius of gyration is a measure related to this distribution.
Torque and rotational equilibrium
Torque is the rotational analogue of force, causing angular acceleration, and equilibrium occurs when the net torque on a body is zero.
Center of mass: definition and calculation
The center of mass is the point representing the mean position of the mass in a system, and can be calculated for discrete particles or continuous bodies.
Rotational kinematics and dynamics
Rotational kinematics describes the motion of rotating bodies, while dynamics relates torque, angular acceleration, and rotational kinetic energy.
Centre of Mass of Discrete Particles
For discrete particles, the centre-of-mass position is the vector sum of each mass times its position divided by total mass; this point governs translation even when the particles move relative to one another.