Torque Vector and Lever Arm
The torque of a force about an origin is tau = r cross F, with magnitude equal to force times perpendicular lever arm and direction fixed by the right-hand rule.
Why this shows up in the exam
Turning a wrench · Finding torque from an oblique force · Comparing forces applied at different points
Learn the idea
Torque measures a force's turning effectiveness through the cross product of position and force. Torque measures a force's turning effectiveness through the cross product of position and force. 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: Only the force component across the radius turns.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- tau_O = r cross F — Vector torque about origin O.
- |tau| = r F sin phi = F d_perp — Torque magnitude using included angle or lever arm.
How to approach it
- 1Choose the torque origin
- 2Draw r to the point of application
- 3Use the perpendicular component and right-hand-rule sign
Common slip-ups that cost marks
- •Using distance along the force line
- •Reversing r cross F
- •Computing torque without naming the origin
🌟 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.