Torque Examples: 47 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Torque.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The rotational equivalent of force; a measure of how much a force tends to cause an object to rotate about an axis.

How hard you're twisting something. Depends on force AND distance from pivot.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Torque asks students to choose the object, list external interactions, and reason from the resulting force or torque pattern.

Common stuck point: Students often know a formula related to torque but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Have I isolated one system and listed the external forces or torques acting on it before applying a law?

Worked Examples

Example 1

easy

A force of

20 \text{ N}

is applied at the end of a

0.5 \text{ m}

wrench, perpendicular to the wrench. What is the torque produced?

Answer

τ = 10 N m

First step

Torque is the rotational equivalent of force:

\tau = rF\sin\theta

Full solution

2
Since the force is perpendicular to the lever arm, $\theta = 90°$ and $\sin 90° = 1$ .
3
$τ = r F = 0.5 \times 20 = 10 N m$

Torque measures the tendency of a force to cause rotation. It depends on the force magnitude, the distance from the pivot point, and the angle between the force and the lever arm.

Example 2

medium

3 \text{ m}

seesaw has a pivot at its center. A

30 \text{ kg}

child sits at one end. How far from the center must a

45 \text{ kg}

child sit to balance the seesaw? Use

g = 9.8 \text{ m/s}^2

Example 3

medium

A 30 N force is applied at the end of a 0.4 m wrench at 60\u00b0 to the handle. Calculate the torque.

Example 4

medium

25 \text{ N}

force pulls on a

0.4 \text{ m}

lever at

30°

to the arm. Find the torque.

Example 5

medium

Two forces act on a

2 \text{ m}

horizontal beam pivoted at its center:

15 \text{ N}

downward

0.8 \text{ m}

left of the pivot, and

12 \text{ N}

downward

1.0 \text{ m}

right of the pivot. Find the net torque about the pivot. Take counterclockwise as positive.

Example 6

medium

A uniform

4 \text{ m}

plank weighs

100 \text{ N}

and rests on a single support at its center. A

200 \text{ N}

box sits

1.0 \text{ m}

to the right of the support. What torque does the box produce about the support? Take counterclockwise as positive.

Example 7

medium

1.2 \text{ m}

wide door requires

18 \text{ N}\cdot\text{m}

of torque to open. (a) What perpendicular force is needed at the handle (placed at the edge)? (b) What force would be needed if the handle were placed only

0.4 \text{ m}

from the hinges?

Example 8

hard

On a seesaw

4 \text{ m}

long pivoted at its center, a

40 \text{ kg}

child sits

1.5 \text{ m}

left of the pivot. A second child must balance them by sitting

2.0 \text{ m}

right of the pivot. What mass must the second child have? Use

g = 9.8 \text{ m/s}^2

Example 9

hard

A uniform

3 \text{ m}

ladder of weight

150 \text{ N}

leans against a frictionless wall at

60°

above the horizontal. The floor is rough. Taking torques about the foot of the ladder, find the normal force the wall exerts on the ladder.

Example 10

medium

0.5 \text{ m}

lever arm experiences a

40 \text{ N}

force at

90°

and a

20 \text{ N}

force at

30°

on the same end, both in the same rotational sense. Find the total torque about the pivot.

Example 11

challenge

A uniform sign of mass

12 \text{ kg}

hangs from a horizontal

1.5 \text{ m}

rod attached to a wall. The rod is held up by a cable from the wall to the rod's far end, making

30°

with the rod. Find the tension in the cable. The rod is massless. Use

g = 9.8 \text{ m/s}^2

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

A door (

1 \text{ m}

wide) requires

50 \text{ N m}

of torque to open. What force must be applied at the edge of the door, perpendicular to it?

Example 2

hard

40 \text{ N}

force is applied to a

0.8 \text{ m}

lever arm at an angle of

60°

to the lever. What is the torque? How does this compare to the maximum possible torque with the same force?

Example 3

easy

10

N force acts perpendicular to a wrench

0.2

m from the pivot. Find the torque.

Example 4

easy

A force produces torque

6

\cdot

m at a lever arm of

0.3

m (perpendicular). Find the force.

Example 5

easy

20

N force is applied

0.5

m from a pivot, perpendicular to the arm. Find the torque.

Example 6

easy

A force is applied directly at the pivot point. What torque does it produce?

Example 7

easy

10

N force acts

0.4

m from a pivot at

30^\circ

to the arm. Find the torque.

Example 8

easy

Two children on a seesaw: a

30

N child sits

2

m left of the pivot. What torque does the child create?

Example 9

easy

A door handle is placed far from the hinges rather than near them. Why does this reduce the force needed to open it?

Example 10

easy

A wheel experiences a clockwise torque of

5

\cdot

m and a counterclockwise torque of

5

\cdot

m. What is the net torque?

Example 11

medium

A seesaw has a

40

N child

1.5

m left of the pivot. How far right must a

60

N child sit to balance it?

Example 12

medium

0.3

m wrench applies a

40

N force at

60^\circ

to the handle. Find the torque.

Example 13

medium

A uniform

4

m beam weighs

200

N and rests on a pivot at its center. A

100

N weight hangs

1

m from the pivot. What torque does the weight create about the pivot?

Example 14

medium

2

m horizontal beam is hinged at the wall. A

50

N weight hangs at the far end, and a vertical cable at the end holds it up. Find the cable tension (massless beam).

Example 15

medium

3

kg uniform rod (

2

m long) is pivoted at one end (

g=10

m/s

^2

). Find the torque due to gravity about the pivot when horizontal.

Example 16

medium

Two forces on a bar:

20

N at

0.5

m (clockwise) and

10

N at

1.5

m (counterclockwise) from the pivot, both perpendicular. Find the net torque.

Example 17

medium

A meter stick is pivoted at the

0.3

m mark. A

6

N weight hangs at the

0

mark. What torque does it create about the pivot?

Example 18

medium

A solid disk (moment of inertia

0.5

\cdot

^2

) has a net torque of

2

\cdot

m. Find its angular acceleration.

Example 19

medium

50

N force is applied

0.6

m from a pivot, perpendicular to the arm. Find the torque.

Example 20

challenge

5

m uniform beam weighs

100

N, supported at both ends. A

300

N load sits

1

m from the left end. Find the right support force.

Example 21

challenge

6

m ladder (

200

N) leans against a frictionless wall at

60^\circ

to the ground. Find the wall's normal force (floor has friction).

Example 22

challenge

4

m beam is hinged at the wall and held by a cable at the far end making

30^\circ

with the beam. A

120

N weight hangs at the end (massless beam). Find the cable tension.

Example 23

easy

A mechanic pushes with

80 \text{ N}

perpendicular to a

0.25 \text{ m}

wrench. What torque is applied to the bolt?

Example 24

easy

50 \text{ N}

force is applied

0.6 \text{ m}

from the pivot, perpendicular to the lever. Find the torque.

Example 25

medium

A wrench is

0.3 \text{ m}

long. To loosen a bolt requires

24 \text{ N}\cdot\text{m}

. What perpendicular force is needed at the end?

Example 26

easy

0.5 \text{ m}

lever arm experiences a

40 \text{ N}

perpendicular force. Find the torque about the pivot.

Example 27

medium

A force of

60 \text{ N}

is applied parallel to a

0.4 \text{ m}

lever arm (along its length). What is the torque?

Example 28

hard

A uniform

6 \text{ m}

beam of weight

200 \text{ N}

is hinged at the left wall and held horizontal by a vertical rope at the right end. What tension does the rope exert? Use

g

already in the weight.

Example 29

medium

0.6 \text{ m}

wrench is used at

45°

to the handle with a

50 \text{ N}

force. Find the torque.

Example 30

easy

5 \text{ kg}

mass hangs from the end of a

0.8 \text{ m}

horizontal rod fixed to a wall. What torque does the weight produce about the wall? Use

g = 9.8 \text{ m/s}^2

Example 31

medium

A child applies

25 \text{ N}

60°

to a

0.5 \text{ m}

pedal arm. What is the torque on the crank?

Example 32

easy

If you double the lever arm but keep the perpendicular force the same, what happens to the torque?

Example 33

medium

A bolt requires

35 \text{ N}\cdot\text{m}

to loosen. You only have a

0.2 \text{ m}

wrench. What perpendicular force must you apply?

Example 34

easy

15 \text{ N}

force is applied perpendicular to a

0.1 \text{ m}

screwdriver shaft. Find the torque on the screw.

Example 35

medium

Two equal

20 \text{ N}

forces act on opposite sides of a

0.4 \text{ m}

wide disc, in opposite directions, both tangent to the disc. What is the net torque about the center?

Example 36

hard

80 \text{ kg}

painter stands

1 \text{ m}

from the left end of a

4 \text{ m}

uniform plank weighing

200 \text{ N}

supported by two sawhorses, one at each end. Find the upward force from the right sawhorse. Use

g = 9.8 \text{ m/s}^2

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Related Concepts

Force Circular Motion Angular Momentum Rotational Equilibrium

Background Knowledge

These ideas may be useful before you work through the harder examples.

forcecircular motion