Work-Energy in Fixed-Axis Rotation
For a rigid body constrained to rotate about a fixed axis, the work of all external torques equals the change in one-half I omega squared; conservative-force work may instead be handled through potential energy.
Why this shows up in the exam
Rods falling about hinges · Rotating bodies driven by gravity · Finding speed after a torque acts through an angle
Learn the idea
Net torque work changes rotational kinetic energy, often simplifying gravity-driven rotation. Net torque work changes rotational kinetic energy, often simplifying gravity-driven rotation. 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: Torque work becomes spin energy.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- W_net = Delta[(1/2) I omega²] — Rotational work-energy theorem for constant I.
- K_i + U_i + W_nc = K_f + U_f — Energy balance including nonconservative work.
How to approach it
- 1Choose the initial and final configurations
- 2Track centre-of-mass potential energy and torque work
- 3Solve for angular speed using inertia about the pivot
Common slip-ups that cost marks
- •Conserving energy through an inelastic impact
- •Using centre-of-mass height incorrectly
- •Forgetting work by external friction or motors
🌟 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.