How to Solve Torque Problems- Practical Physics Examples

What Torque Actually Is (And Why Students Get It Wrong)

Torque is a rotational force. That's it. While force makes objects accelerate linearly, torque makes them spin. Most students bomb torque problems because they try to memorize formulas without understanding the concept first.

Think of a wrench loosening a bolt. The longer the wrench, the easier it is to turn the bolt. That's torque in action. More distance from the pivot point means more rotational effect with the same force.

The Torque Formula You Actually Need

The standard equation is:

τ = r × F × sin(θ)

Where:

• τ = torque (measured in newton-meters, N·m)
• r = distance from pivot point to where force is applied
• F = magnitude of the force
• θ = angle between the force direction and the lever arm

The sin(θ) part trips people up. When the force pushes perpendicular to the lever arm (θ = 90°), sin(90°) = 1, so you just multiply r × F. Most textbook problems set up perpendicular forces for simplicity.

Direction of Torque: The Sign Convention

Torque has direction. Physics textbooks usually call:

• Counterclockwise (CCW) torque positive
• Clockwise (CW) torque negative

This matters when setting up equilibrium equations. If two forces produce torques in opposite directions, they can cancel out.

How to Solve Torque Problems: A Step-by-Step Approach

Step 1: Identify the Pivot Point

The pivot is your reference point. Choose it strategically. Often it's a fulcrum, hinge, or axle. Sometimes the problem doesn't specify—you pick whichever makes calculations easiest.

Pro tip: Place your pivot at the point where forces are unknown. This eliminates that force's torque from your equation since r = 0.

Step 2: Draw Your Lever Arms

For each force, draw a line from the pivot to the point of application. Measure the perpendicular distance from this line to the force's line of action.

If the force is perpendicular to the lever arm, the lever arm equals the full distance r. If not, you'll need the perpendicular component.

Step 3: Determine the Torque Direction

Ask yourself: will this force make the object rotate clockwise or counterclockwise around the pivot?

Use the right-hand rule if needed: point your fingers along r, curl them toward F, and your thumb points in the torque direction.

Step 4: Set Up Your Equilibrium Equation

For static equilibrium problems:

Στ = 0

Sum all torques, with signs, and set equal to zero. Solve for your unknown.

Practical Example #1: The Seesaw Problem

A 40 N child sits 2 m from the pivot of a seesaw. Where must a 60 N child sit to balance it?

Solution:

Child 1 torque (CCW, positive): τ₁ = (2 m)(40 N) = 80 N·m

For equilibrium: τ₁ + τ₂ = 0

80 + (-60)(r₂) = 0

r₂ = 80/60 = 1.33 m

The 60 N child sits 1.33 m from the pivot on the opposite side.

Practical Example #2: Wrench Problem

A mechanic applies 200 N of force at the end of a 0.4 m wrench at a 60° angle to the handle. What torque is produced?

Solution:

τ = rF sin(θ) = (0.4 m)(200 N)(sin 60°)

τ = 0.4 × 200 × 0.866 = 69.3 N·m

Note: If the force were perfectly perpendicular (90°), sin(90°) = 1, giving τ = 80 N·m. The angled force reduces effective torque.

Practical Example #3: Beam Supported at One End

A uniform beam (weight W, length L) is supported at one end by a hinge. A box (weight 2W) sits at the far end. Find the tension in the support cable.

Solution:

Take torques about the hinge. The hinge force produces zero torque (r = 0), so it vanishes from the equation.

Beam weight acts at L/2, box weight at L:

CW torques (negative): τ = -(W)(L/2) - (2W)(L) = -2.5WL

Tension acts upward through the cable, creating CCW torque. The lever arm is the vertical distance from hinge to cable attachment.

Set Στ = 0 and solve for T based on your cable geometry.

Common Mistakes That Cost You Points

• Using the wrong angle: Always use the angle between the force and the lever arm (r), not the angle from horizontal
• Forgetting sign conventions: Pick a direction convention and stick to it consistently
• Measuring from the wrong point: r is always from pivot to where force is applied
• Confusing mass and weight: Weight = mg, not just m
• Units errors: Keep everything in meters, Newtons, and N·m

Torque vs. Moment of Inertia: Know the Difference

Students confuse these constantly.

The relationship between them: τ = Iα, where α is angular acceleration. This is the rotational equivalent of F = ma.

Quick Reference: When to Use What

Getting Started: Your First Torque Problem

Here's a simple checklist before you start:

• Circle the pivot point in your diagram
• Draw each force's lever arm clearly
• Label the perpendicular distance for each force
• Assign + or - based on rotation direction
• Write Στ = 0 (for equilibrium)
• Solve algebraically before plugging numbers

Work through three problems using this checklist and it'll click. Torque isn't hard—students just overcomplicate it.