Force: Turning Effect and Circular Motion notes: ICSE Class 10 Physics (Science Paper 1)

1. Translational and rotational motion; moment of a force

Translational motion: every particle moves the same distance in the same direction. Rotational motion: the body turns about a fixed axis.
A force on a pivoted body turns it; its turning effect is the moment of the force (torque): $\tau = F \times d$ , $d$ = perpendicular distance from the axis to the line of action.
Units: N m (SI), dyne cm (cgs); $1\ \text{N m} = 10^{7}\ \text{dyne cm}$ .
Moment increases with force and with perpendicular distance: handles far from hinges, long spanners, large steering wheels. A force through the axis has zero moment.

Table showing that equal moments can come from different force and distance pairs
F	d	Moment
20 N	0.5 m	10 N m
10 N	1.0 m	10 N m
40 N	0 m	0

Formulas

Moment of a force
$\tau = F \times d$
Unit conversion
$1\ \text{N m} = 10^{7}\ \text{dyne cm}$

Key terms

Moment of a force: The turning effect of a force about an axis, equal to the force multiplied by the perpendicular distance of its line of action from the axis.
Rotational motion: Motion in which a body turns about a fixed axis, each particle moving in a circle.

2. Clockwise and anticlockwise moments; couples

Convention: anticlockwise moments positive, clockwise negative.
Resultant moment = algebraic sum; the body turns in the sense of the larger total.
Couple: two equal, opposite, parallel forces not in the same line; produces rotation only. Moment of couple = $F \times$ arm (perpendicular distance between the forces). Examples: tap, steering wheel, winding a key.

Table of the sign convention for moments
Moment	Sense	Sign
Turns like clock hands	Clockwise	Negative
Turns the other way	Anticlockwise	Positive

Formulas

Moment of a couple
$\tau_{\text{couple}} = F \times \text{arm}$

Key terms

Couple: Two equal and opposite parallel forces whose lines of action are different; it produces rotation only.
Resultant moment: The algebraic sum of the moments of all the forces about a point.

3. Equilibrium and the principle of moments

Equilibrium: a body at rest (static) or moving with uniform velocity without turning faster (dynamic). Conditions: (1) resultant force = 0; (2) resultant moment = 0.

Principle of moments: for a body in equilibrium, sum of anticlockwise moments about any point = sum of clockwise moments about that point: $W_{1} d_{1} = W_{2} d_{2}$ .

Verification: metre rule on a knife edge, weights hung on both sides, adjusted until the rule is horizontal; products W × d agree. Take moments about the fulcrum; include the rule’s weight at its centre of gravity if it is not pivoted there.

Table of the two conditions of equilibrium
Condition	Prevents
Resultant force zero	Translation
Resultant moment zero	Rotation

Formulas

Balanced lever
$W_{1} d_{1} = W_{2} d_{2}$

Key terms

Principle of moments: For a body in equilibrium, the sum of the anticlockwise moments about any point equals the sum of the clockwise moments about that point.
Static equilibrium: The state of a body at rest under several forces.

4. Centre of gravity

Centre of gravity (G): the point through which the whole weight of a body acts, in every orientation. It may lie outside the material (ring).

Body	Position of G
Uniform rod	Mid-point
Ring	Centre of the ring
Circular disc	Centre
Triangular lamina	Point of intersection of the medians
Rectangle, parallelogram	Intersection of the diagonals

Irregular lamina: suspend freely from a hole with a plumb line, mark the vertical; repeat from a second hole; G is where the lines cross.

Table of centres of gravity of three regular shapes
Shape	G
Rod	Middle
Ring	Centre (in air)
Triangle	Medians meet

Key terms

Centre of gravity: The point through which the whole weight of a body acts, whatever its position.

5. Uniform circular motion

Uniform circular motion: constant speed along a circle; velocity is along the tangent and changes direction continuously, so the motion is accelerated.
Centripetal force: the real force towards the centre that keeps the body in the circle (tension, gravity, friction, electrostatic attraction).
Centrifugal force: the apparent outward force felt in the rotating frame; fictitious, equal and opposite to the centripetal force.
If the centripetal force stops, the body moves off along the tangent (mud flying off a cycle wheel).

Table of three circular motions and their centripetal forces
Motion	Centripetal force from
Moon round Earth	Gravity
Car on a bend	Friction
Stone on string	Tension

Key terms

Centripetal force: The force directed towards the centre that keeps a body moving in a circle.
Centrifugal force: An apparent outward force felt by a body in a rotating frame; it is not a real force.

Exam tips

Common mistakes

Using the length along a body instead of the perpendicular distance.
Forgetting to convert cm to m for N m answers.
Ignoring the weight of a metre rule pivoted away from its centre.
Saying uniform circular motion is not accelerated.

How marks are usually awarded

Calculations (1 mark each step): formula, substitution with units, answer with unit and sense.
Definitions (1 mark): include “perpendicular distance”, “about any point”, “whole weight acts”.
Circular motion (1 mark each): direction of velocity and of centripetal force.

1. Translational and rotational motion; moment of a force

Formulas

Key terms

2. Clockwise and anticlockwise moments; couples

Formulas

Key terms

3. Equilibrium and the principle of moments

Formulas

Key terms

4. Centre of gravity

Key terms

5. Uniform circular motion

Key terms

Exam tips

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