Last Updated on May 14, 2026 by sanjjeett
Chapter 1: Force
Core Concepts
Turning Effect of Force (Moment of Force)
The turning effect of a force about a point is called the Moment of Force or Torque. It is the tendency of a force to rotate a body about a fixed point or axis.
- Moment of Force = Force × Perpendicular distance from the pivot
- SI Unit: Newton-metre (N·m)
- It is a vector quantity
- Clockwise moment is taken as negative; Anticlockwise moment as positive
Practical examples: Opening a door, using a spanner, a see-saw, steering wheel of a car.
Couple and Torque of a Couple
A couple consists of two equal, opposite, and parallel forces acting on a body along different lines of action. A couple always produces a turning effect only — it never produces translational motion.
- Torque of a couple = Either force × Perpendicular distance between the two forces
- The torque of a couple is the same about every point in its plane
- A couple cannot be balanced by a single force — only by another couple of equal and opposite torque
Practical examples: Turning a key in a lock, winding a watch, rotating a water tap, using a steering wheel.
Principle of Moments (Conditions of Equilibrium)
A body is in equilibrium when the net force and net torque are both zero. Two conditions must be satisfied:
- First condition: Algebraic sum of all forces = zero (no translation)
- Second condition: Sum of Clockwise Moments = Sum of Anticlockwise Moments (no rotation)
Types of Equilibrium
- Stable: Body returns to original position. CG rises on displacement. Wide base, low CG. Example: Cone on base.
- Unstable: Body moves further away. CG falls on displacement. Example: Cone on tip.
- Neutral: Body stays in new position. CG remains at same height. Example: Cone on side.
Centre of Gravity
The centre of gravity (CG) is the point through which the resultant gravitational force acts, regardless of the body’s position or orientation.
- For a uniform body, CG lies at its geometric centre
- CG of an irregular body (e.g. L-shape) may lie outside the material
- Lower the CG and wider the base → more stable
Uniform Circular Motion
When a body moves in a circular path with constant speed, it undergoes uniform circular motion. Speed is constant but velocity changes continuously (direction changes) — so the body is accelerating.
- Centripetal acceleration → directed towards the centre
- Centripetal force → directed towards the centre, keeps body in circle
- Centripetal force is not a new force — provided by gravity, tension, friction etc.
- Centrifugal force → pseudo force, acts outward in rotating frame only
Important Definitions
Formulas to Remember
Differentiate Between
| Basis | Force (Single) | Couple |
|---|---|---|
| Definition | A single push or pull on a body | Two equal, opposite, parallel forces on a body |
| Effect | Translational + rotational motion | Rotational motion only |
| Net force | Has a net resultant force | Net resultant force is zero |
| Balanced by | A single equal and opposite force | Only by another couple |
| Basis | Stable | Unstable | Neutral |
|---|---|---|---|
| On displacement | Returns to original position | Moves further away | Stays in new position |
| CG on displacement | Rises | Falls | Same height |
| CG position | Lowest possible | Highest possible | Neither rises nor falls |
| Example | Cone on base | Cone on tip | Cone on side |
Give Reasons
A racing car has a low height and a wide wheelbase. Give reason.
A racing car is built low to keep its centre of gravity as low as possible, and wide to have a broad base. Both factors increase stability and reduce the chance of toppling during high-speed turns.
A couple cannot be balanced by a single force. Give reason.
A couple has net resultant force = zero but produces a net torque. A single force always has a resultant, so it cannot simultaneously produce zero net force and a net torque. Hence a couple can only be balanced by another couple of equal and opposite torque.
It is easier to open a door by pushing at the end far from the hinge. Give reason.
Moment of force = Force × Perpendicular distance from pivot. Applying force at the far end maximises the perpendicular distance from the hinge, so the moment of force is maximum for the same applied force — making it easier to rotate the door.
A body moving in a circular path with constant speed is still said to be accelerating. Give reason.
Acceleration is the rate of change of velocity, not speed. In circular motion, although speed is constant, the direction of velocity changes continuously. Since velocity is a vector, any change in direction is a change in velocity — hence the body is continuously accelerating (centripetal acceleration, directed towards the centre).
The CG of an L-shaped lamina lies outside its material. Give reason.
For an L-shaped lamina, the geometric centre (where CG would lie for a uniform shape) falls in the empty region between the two arms of the L. Since there is no material at that point, the CG lies outside the material of the body.
Passengers are not allowed to stand in the upper deck of a double-decker bus. Give reason.
Standing passengers in the upper deck raise the centre of gravity of the bus. A higher CG reduces stability and increases the risk of toppling, especially while turning or on uneven roads. To maintain safety, standing in the upper deck is not permitted.
Diagrams to Know
State the Principle of Moments. A uniform metre rule is balanced at 30 cm when a weight of 40 gf is at 10 cm mark. Find the weight of the metre rule.
Principle of Moments: When a body is in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about any point.
CG of metre rule = 50 cm. Balanced at 30 cm.
ACW moment = 40 × (30 − 10) = 800 gf·cm
CW moment = W × (50 − 30) = W × 20
W × 20 = 800 → W = 40 gf
Differentiate between stable and unstable equilibrium with one example each.
Stable: Body returns to original position after displacement. CG rises. Example: Cone on base.
Unstable: Body moves further away after displacement. CG falls. Example: Cone on tip.
What is a couple? Give two examples of couple in daily life.
A couple consists of two equal, opposite, and parallel forces acting on a body at different points along different lines of action. Net force = zero. Produces only rotational motion.
Examples: (1) Turning a key in a lock. (2) Turning a water tap.