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📘 Lesson 15 of 19 · Mechanics

🔧 Torque

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.

Course progress: 79%

01 Key Concepts

Torque 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.

Lever 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.

Direction of Torque

Torque can be clockwise or counterclockwise; by convention, counterclockwise is often treated as positive.

Newton'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.

Rotational 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).

02 Key Formulas

03 Solved Examples

Example 1 A 20 N force is applied perpendicular to a wrench, 0.3m from the bolt. Find the torque.
  1. Since the force is perpendicular, theta=90°, sin(90°)=1.
  2. tau = F*r*sin(theta) = 20*0.3*1.
Answer: 6 N*m
Example 2 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.
  1. Apply tau = F*r*sin(theta) = 15*0.5*sin(30°).
  2. = 7.5*0.5.
Answer: 3.75 N*m
Example 3 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)?
  1. Set the torques equal: 400*2 = 200*d.
  2. 800 = 200d, so d = 800/200.
Answer: 4 meters

04 Practice Questions

1A 10 N force is applied perpendicular to a wrench, 0.2m from the bolt. Find torque.
2 N*m
2A 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
3What does 'lever arm' refer to?
The perpendicular distance from the axis of rotation to the line of action of a force
4What is the rotational equivalent of F=ma?
tau = I*alpha
5What does 'rotational equilibrium' mean?
The net torque on an object is zero

📄 Torque — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet