AICE Physics Torque- Practice Problems and Solutions

What Is Torque and Why It Matters in AICE Physics

Torque is the rotational equivalent of force. While force causes linear acceleration, torque causes angular acceleration. In AICE Physics, you need to understand how to calculate it, apply it to equilibrium problems, and avoid the stupid mistakes that cost students easy marks.

The formula is simple:

τ = r × F × sin(θ)

Where:

• τ = torque (Nm)
• r = perpendicular distance from pivot to line of action (m)
• F = applied force (N)
• θ = angle between r and F

The Key Thing Most Students Miss

You have two ways to calculate torque:

1. Using the full formula: τ = rF sin(θ)
2. Using perpendicular distance: τ = F × d, where d is the shortest distance from the pivot to the line of action of the force

Method 2 is usually faster. Find the shortest distance, multiply by the force. Done.

Practice Problems

Problem 1: Basic Torque Calculation

A wrench 0.30 m long is used to loosen a bolt. A force of 200 N is applied at the end, perpendicular to the wrench handle.

Find the torque produced.

Solution:

Since the force is perpendicular to the wrench (θ = 90°, sin 90° = 1):

τ = rF sin(θ)
τ = (0.30 m)(200 N)(1)
τ = 60 Nm

Problem 2: Force at an Angle

A door is 0.90 m wide. A force of 50 N is applied at the handle at 30° to the door surface.

Calculate the torque about the hinges.

Solution:

The perpendicular distance is the door width (0.90 m) because the force is applied at the handle, which is the farthest point from the hinge.

τ = rF sin(θ)
τ = (0.90 m)(50 N)(sin 30°)
τ = (0.90)(50)(0.5)
τ = 22.5 Nm

Alternatively, using the perpendicular component of force:

F⊥ = F sin(30°) = 50 × 0.5 = 25 N
τ = r × F⊥ = 0.90 × 25 = 22.5 Nm

Problem 3: Equilibrium Condition

A uniform beam of mass 5 kg and length 3 m rests on a support at its midpoint. A 20 N weight is hung 0.5 m from the left end.

Find where a second weight of 30 N must be hung to achieve rotational equilibrium.

Solution:

For equilibrium, net torque must be zero. Take moments about the support (midpoint).

Clockwise torque = Counterclockwise torque

Weight 1 produces clockwise torque:
τ₁ = (1.5 m - 0.5 m) × 20 N = 1.0 × 20 = 20 Nm clockwise

Weight 2 must produce counterclockwise torque:
τ₂ = x × 30 N

For equilibrium:
30x = 20
x = 0.67 m from the support on the opposite side

So the 30 N weight hangs 0.67 m from the support toward the right end, or 2.17 m from the left end.

Problem 4: Maximum and Minimum Torque

A force F is applied to a lever arm of length r. At what angle should the force be applied to produce:

• (a) Maximum torque
• (b) Minimum torque

Solution:

From τ = rF sin(θ):

• Maximum torque occurs when sin(θ) = 1, so θ = 90° (force perpendicular to lever)
• Minimum torque is zero when sin(θ) = 0, so θ = 0° or 180° (force along the line of the lever)

Common Mistakes That Lose Marks

• Using the wrong distance. Students often use the full length instead of the perpendicular distance to the line of action.
• Forgetting to resolve components. When force isn't perpendicular, either use sin(θ) or find the perpendicular component. Don't do both.
• Sign errors in equilibrium. Clockwise and counterclockwise torques must cancel. Label your directions clearly.
• Confusing torque with work. Torque has units Nm. Work also has units Nm (joules), but they're different quantities. Don't write torque in joules.

Quick Reference Table

Getting Started: How to Solve Any Torque Problem

1. Identify the pivot point. Usually given or obvious (hinges, fulcrum, support).
2. Find the perpendicular distance from the pivot to where the force acts.
3. Determine the angle between the force direction and the lever arm.
4. Calculate torque using τ = rF sin(θ) or τ = Fd.
5. Check direction. Assign positive for one direction (clockwise or CCW), negative for the other.
6. For equilibrium: Sum of torques = 0. Solve for the unknown.

What to Memorize

You need these for the exam:

• τ = rF sin(θ)
• Maximum torque when θ = 90°
• Zero torque when θ = 0° or 180°
• Rotational equilibrium: Στ = 0

That's it. Practice the problems above until you can do them without looking at the solutions.