Rotational Dynamics about a Fixed Axis
For a rigid body rotating about a fixed principal axis, the algebraic net external torque about that axis equals the moment of inertia about the same axis times angular acceleration.
Why this shows up in the exam
Accelerating pulleys and flywheels · Finding angular acceleration from applied forces · Coupling translation to drum rotation
Learn the idea
Net external torque changes angular velocity according to the body's moment of inertia. Net external torque changes angular velocity according to the body's moment of inertia. 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 is rotational force; inertia is rotational mass.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum tau_axis = I_axis alpha — Fixed-axis rotational equation of motion.
- alpha = tau_net/I — Angular response for constant I about the selected axis.
How to approach it
- 1Select the body and axis
- 2Sum signed external torques about that axis
- 3Use the matching moment of inertia and kinematic constraints
Common slip-ups that cost marks
- •Using inertia about a different axis
- •Omitting torque signs
- •Applying tau=I alpha to an axis that is translating without accounting for it
🌟 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.