Short on time? This page is the recap. For explanations, diagrams and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- Model the object as a rigid system: its shape does not change, so one angle describes its rotation.
- Choose and state the axis of rotation. Every torque is measured about that axis.
- Torque measures how strongly a force tends to turn the object. It depends on the size of the force, where it acts and its direction.
- Only the force component perpendicular to r (the line from the axis to the point of application) causes turning. The component along r does nothing to the rotation.
- The lever arm is the perpendicular distance from the axis to the force’s line of action.
- A force diagram is a free-body diagram in which each force is drawn at the point where it acts. Weight acts at the centre of mass.
- Label each torque clockwise or counterclockwise for bookkeeping. The vector direction of torque is not part of this course.
Key relationships
| Relationship | Symbols and units | Use it when |
|---|---|---|
| τ = rF sin θ | r in m, F in N, θ between r and F; τ in N·m | you know r, F and the angle |
| τ = rF⊥, with F⊥ = F sin θ | F⊥ in N | the force is already split into components |
| τ = r⊥F, with r⊥ = r sin θ | r⊥ in m | the line of action is easy to draw |
| τ = 0 | the force acts at the axis, or its line of action passes through it | |
| τ_new / τ_old = (F ratio)(r ratio)(sin θ ratio) | a factor-of-change question |
Assumptions behind the numbers
- The object is rigid: forces do not bend or stretch it.
- Each force acts at a single point. Gravity on a rigid object acts at its centre of mass; for a uniform rod, its middle.
- Near Earth’s surface, g = 9.8 m/s².
- The angle θ is measured between the vectors r and F placed tail to tail.
Mistakes to avoid
- No axis stated. The same force has different torques about different axes.
- Using r instead of the lever arm when the force is not at 90° to r.
- Using the wrong angle. Convert any angle “to the surface” or “to the vertical” into the angle between r and F.
- Ignoring forces at the axis. They are on the force diagram, but their torque about that axis is zero.
- Drawing all forces from the centre. For torque, draw each force where it acts.
- Writing joules instead of N·m.
- Calculator in radians when the angle is in degrees.
Quick self-check
- A 25 N force acts at right angles to a rod, 0.40 m from the axis. Find the torque. (10 N·m)
- A 30 N force acts 0.50 m from the axis at 30° to r. Find the torque. (7.5 N·m)
- A rope pulls on a pole with its line of action passing straight through the pivot. What torque does it exert about the pivot? (Zero: the lever arm is zero.)
Next: practice questions.