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Turning effect of forces: Class 9 Physics
Torque or moment of a force, the principle of moments, centre of mass and centre of gravity, the two conditions of equilibrium, types of equilibrium, and stability of bodies.
Key points
A force can turn a body about a fixed point or line called the pivot or axis of rotation. Opening a door, using a spanner and pushing a see-saw all show the turning effect of a force. The turning effect depends on the size of the force and on how far the force acts from the pivot.
The moment of a force, also called torque, is the product of the force and the perpendicular distance from the pivot to the line of action of the force: τ = F × d. Its SI unit is the newton metre (N m). The distance d is the moment arm. It must be measured at a right angle to the force.
Torque is easy to see in daily life:
- A door is easier to open when pushed far from the hinges, where d is large.
- A long spanner loosens a tight nut more easily than a short one.
- A force applied through the pivot has d = 0, so its moment is zero.
By convention, a moment that turns a body anticlockwise is called positive and a clockwise moment is called negative. Using this rule, the total moment is found by adding the moments with their signs.
The principle of moments: when a body is in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point. For a uniform metre rule balanced on a knife edge, a weight W₁ at distance d₁ on one side balances W₂ at distance d₂ on the other when W₁d₁ = W₂d₂.
A couple is a pair of equal and opposite parallel forces that do not act along the same line. It produces rotation without any net force. The moment of a couple is one of the forces times the perpendicular distance between them. Turning a steering wheel with two hands and opening a tap are examples of couples.
Equilibrium means that a body has no change in its state of motion. A body in equilibrium has zero linear acceleration and zero angular acceleration. A body at rest is in static equilibrium. A body moving with constant velocity is also in equilibrium.
There are two conditions of equilibrium:
- First condition: the vector sum of all forces on the body is zero (ΣF = 0). This stops linear acceleration.
- Second condition: the sum of all torques about any point is zero (Στ = 0). This stops rotation.
The centre of mass of a body is the point where its whole mass can be taken as concentrated for motion. The centre of gravity is the point through which the whole weight of the body acts. In a uniform gravity field they are the same point. For a uniform rod it is the midpoint. For a circular ring or disc it is the centre. For a rectangular sheet it is where the diagonals meet. For a triangular sheet it is where the medians meet.
To find the centre of gravity of an irregular flat sheet, hang it freely from a pin at one hole and draw a vertical line with a plumb line. Repeat from a second and a third hole. The lines cross at the centre of gravity. The centre of gravity of a body may lie outside the material, as for a ring.
There are three types of equilibrium:
- Stable: when slightly tilted, the body returns to its first position. Its centre of gravity rises when tilted, like a cone resting on its base.
- Unstable: when slightly tilted, it moves further away. Its centre of gravity falls, like a cone balanced on its tip.
- Neutral: when moved, it stays in its new position. The centre of gravity stays at the same height, like a ball on a table.
A body is more stable when its base is wide and its centre of gravity is low. A body topples when the vertical line from its centre of gravity falls outside its base. This is why racing cars are built low and wide, why buses with passengers on the upper deck are risky on slopes, and why the leaning tower of Pisa does not fall: the vertical line from its centre of gravity still falls inside its base.
Study tip: Always mark the pivot first, then list each force with its distance from the pivot. Write clockwise and anticlockwise moments in two separate lines before equating them. In theory questions, draw a small diagram and name the pivot, forces and distances clearly.
Definitions and flashcards
Say the meaning first, then open the card to check.
Torque
The turning effect of a force, equal to force times perpendicular distance from the pivot.
Moment arm
The perpendicular distance from the pivot to the line of action of the force.
Couple
Two equal and opposite parallel forces acting along different lines.
Equilibrium
The state of a body with no linear or angular acceleration.
Centre of mass
The point where the whole mass of a body can be taken as concentrated.
Centre of gravity
The point through which the weight of a body acts.
Stable equilibrium
A body returns to its position after a small tilt.
Unstable equilibrium
A body moves further away from its position after a small tilt.
Neutral equilibrium
A body stays in the new position after a small displacement.
Formula sheet
| Name | Formula | What it means |
|---|---|---|
| Torque | τ = F × d | Force times perpendicular distance from the pivot |
| Principle of moments | Clockwise moments = anticlockwise moments | Condition for balance about a pivot |
| First condition of equilibrium | ΣF = 0 | Net force is zero |
| Second condition of equilibrium | Στ = 0 | Net torque is zero |
| Moment of a couple | τ = F × d | One force times the distance between the two forces |
Short questions with model answers
These are the kind of questions asked for 2, 3 and 5 marks. Try each one before opening the answer.
Define torque and state its SI unit. (2 marks)
Torque is the turning effect of a force about a pivot. It equals the force multiplied by the perpendicular distance from the pivot to the line of action of the force. Its SI unit is the newton metre (N m).
Why is it easier to open a door by pushing at the handle than near the hinges? (2 marks)
Torque is force times distance from the hinge. The handle is far from the hinge, so the distance is large. A smaller force then gives the needed torque. Near the hinge the distance is small, so a much larger force is required.
What is a couple? Give two examples. (3 marks)
A couple is a pair of equal and opposite parallel forces that act along different lines. It turns a body without moving it as a whole. Its moment equals one force times the perpendicular distance between the two lines. Examples are turning a steering wheel with both hands and turning a water tap.
State the two conditions of equilibrium. (3 marks)
First, the vector sum of all forces acting on the body must be zero, so that it has no linear acceleration. Second, the sum of all torques about any point must be zero, so that it has no angular acceleration. Clockwise and anticlockwise torques must therefore be equal.
Describe how to find the centre of gravity of an irregular sheet of cardboard. (5 marks)
Make three small holes near the edge of the sheet. Hang the sheet from a pin through one hole so that it swings freely. Hang a plumb line from the same pin and mark its path on the sheet. Repeat from the second and third holes. The lines meet at one point, which is the centre of gravity. The sheet balances at that point on a pencil tip. Three lines are used to check that the point is right.
Explain the three types of equilibrium with examples and say how stability can be increased. (5 marks)
In stable equilibrium a small tilt raises the centre of gravity and the body returns, like a cone on its base. In unstable equilibrium a small tilt lowers the centre of gravity and the body falls further, like a cone on its tip. In neutral equilibrium the centre of gravity stays at the same height and the body rests in its new position, like a rolling ball. Stability is increased by making the base wider and by keeping the centre of gravity low. A body topples when the vertical line from its centre of gravity falls outside its base.
Numericals with worked steps
A force of 40 N acts at the end of a spanner 0.25 m long, at right angles to it. Find the torque.
- F = 40 N, d = 0.25 m
- τ = F × d = 40 × 0.25
- τ = 10 N m
Answer: 10 N m
A uniform metre rule is balanced at the 50 cm mark. A 3 N weight hangs at the 20 cm mark. At which mark must a 2 N weight hang on the other side to balance it?
- Distance of the 3 N weight from the pivot = 50 − 20 = 30 cm
- Anticlockwise moment = 3 × 30 = 90 N cm
- Let the 2 N weight be x cm from the pivot: 2 × x = 90
- x = 45 cm, so the mark is 50 + 45 = 95 cm
Answer: At the 95 cm mark
Two children sit on a see-saw. A 300 N child is 2 m from the pivot. Where must a 400 N child sit to balance on the other side?
- Moment of first child = 300 × 2 = 600 N m
- For balance, 400 × d = 600
- d = 600/400 = 1.5 m
Answer: 1.5 m from the pivot
A couple has two forces of 15 N each, 0.4 m apart. Find the moment of the couple.
- F = 15 N, perpendicular distance = 0.4 m
- Moment = F × d = 15 × 0.4
- = 6 N m
Answer: 6 N m
Common mistakes
- Using the length of the lever instead of the perpendicular distance from the pivot to the line of force.
- Mixing units, such as cm for one distance and m for another, in the same moment equation.
- Saying a couple has a net force. The net force is zero but the net torque is not.
- Thinking the centre of gravity is always inside the body. For a ring or a hollow bowl it lies in the empty space.
- Forgetting to include the weight of a uniform rod, acting at its midpoint, in the moments.