Rotational Motion – Stage 1 (Page 3)

Torque – The Turning Effect of Force

In translational motion, force changes velocity. In rotational motion, torque changes angular velocity. Torque plays the same role in rotation as force plays in linear motion.

1. What is Torque?

Torque is the turning effect of a force about a fixed axis or point.

Examples:
• Opening a door
• Turning a spanner
• Pedaling a bicycle

2. Mathematical Definition of Torque

Torque (τ) = r × F

• r = position vector from axis to point of application of force
• F = applied force
• SI unit: N·m

Important: Torque is a vector quantity.

3. Magnitude of Torque

|τ| = rF sinθ

θ is the angle between r and F.

✔ Maximum torque when θ = 90°
✔ Zero torque when θ = 0° or 180°

4. Moment Arm (Lever Arm)

Moment arm is the perpendicular distance from the axis of rotation to the line of action of force.

Torque = Force × Moment arm

This form is very useful in numerical problems.

5. Direction of Torque

Direction of torque is given by the Right-Hand Rule.

Curl fingers in direction from r to F, thumb gives direction of torque.

6. Physical Meaning of Torque

✔ Same force can produce different torque
✔ Torque depends on point of application
✔ Greater moment arm → easier rotation

⚠ Common Student Mistakes

❌ Using r instead of perpendicular distance ❌ Forgetting angle between r and F ❌ Assuming force always produces rotation

IIT-JEE Insight

IIT problems often test whether students identify the correct axis and correct moment arm before calculating torque.

Next: Stage 1 – Page 4
Torque, Angular Momentum & Rotational Equilibrium

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