Torque
- Define torque as τ = rF sinθ and identify the lever arm
- Explain how distance and angle affect turning effectiveness
- Determine the direction of a torque (clockwise or counterclockwise)
Torque is the turning effect of a force
Torque measures how effectively a force rotates an object about an axis. It depends on three things: the size of the force, how far from the axis it acts (r), and the angle at which it is applied. Push on a door near its hinge and little happens; push at the far edge and it swings easily. Torque, not force alone, is what causes angular acceleration.
The lever arm and the best angle
Only the component of the force perpendicular to the line from the axis produces torque, so τ = rF sinθ. The quantity r sinθ is the lever arm — the perpendicular distance from the axis to the line of the force. Torque is largest when the force is applied at 90° (sinθ = 1) and farthest from the axis; a force aimed straight at the axis produces no torque at all.
A mechanic pushes with 40 N perpendicular to a wrench, gripping it 0.25 m from the bolt. Find the torque on the bolt.
- 1.The force is perpendicular, so θ = 90° and sinθ = 1.
- 2.Torque: τ = rF sinθ = 0.25 × 40 × 1.
- 3.Compute: τ = 10 N·m.
- 4.Gripping farther out or pushing harder would increase this torque proportionally.
To get the most turn from a limited force, maximize both the distance from the axis and the perpendicularity. That is why a longer wrench loosens a stubborn bolt and why door handles sit as far from the hinge as possible.
A 40 N force is applied perpendicular to a wrench at a point 0.25 m from the bolt. What is the torque?
To open a heavy door with the least force, where and how should you push?
When a force is not perpendicular, do not forget the sinθ. A common error is using τ = rF and ignoring the angle; only the perpendicular component turns the object.
Answer the 2 checkpoints as you read.
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