BitWithBite
Mechanics · Quick Reference
Torque Cheat Sheet
In one line: torque measures the twisting or turning effect of a force — the same push can barely budge a door or swing it wide open, depending on where and how you push.
Key Ideas
1Torque Definition. tau = F*r*sin(theta), where F is the applied force, r is the distance from the pivot (axis) to where the force is applied, and theta is the angle between the force and the lever arm.
2Lever Arm. The perpendicular distance from the axis of rotation to the line of action of the force -- torque is maximized when the force is applied perpendicular to this arm.
3Direction of Torque. Torque can be clockwise or counterclockwise; by convention, counterclockwise is often treated as positive.
4Newton's Second Law for Rotation. The rotational analog of F=ma is tau = I*alpha, where I is moment of inertia and alpha is angular acceleration.
5Rotational Equilibrium. An object is in rotational equilibrium when the net torque acting on it is zero, meaning it has no angular acceleration (it may still be rotating at constant angular velocity, or not rotating at all).
Worked Examples
A 20 N force is applied perpendicular to a wrench, 0.3m from the bolt. Find the torque.
6 N*m
A 15 N force is applied to a lever at a 30° angle, 0.5m from the pivot (sin(30°)=0.5). Find the torque.
3.75 N*m
A seesaw has a 400 N person sitting 2m from the pivot on one side. How far from the pivot on the other side must a 200 N person sit to balance it (equal and opposite torques)?
4 meters
Formulas
tau = F*r*sin(theta)
tau = I*alpha
Practice Yourself
A 10 N force is applied perpendicular to a wrench, 0.2m from the bolt. Find torque.
2 N*m
A seesaw balances with a 300 N person at 2m; find the force needed at 3m on the other side.
300*2=F*3, F=200N
What does 'lever arm' refer to?
The perpendicular distance from the axis of rotation to the line of action of a force