Hello, and welcome to your Class 10 Physics lesson. Today, we begin our exploration of Force — one of the most fundamental concepts in physics. We will journey through three major territories: first, the turning effect of forces and how bodies achieve balance; second, the centre of gravity; and finally, the fascinating world of uniform circular motion. Let us begin.
When a force acts upon a rigid body, the body can respond in two distinct ways. If the body is free to move, it undergoes translational motion — it slides or glides in a straight path following the direction of the applied force. Imagine pushing a ball across a smooth floor; it rolls forward in a straight line. This is translational motion.
But now consider a body that is fixed at a point — a door hinged at one edge, or a wheel anchored at its centre. When force is applied at a suitable point, the body does not translate; instead, it rotates about that fixed point. This is rotational motion. The same force, applied differently, produces entirely different effects.
The turning effect of a force is called its moment of force, also called torque. Think of opening a heavy door. You instinctively push far from the hinges, not near them. Why? Because the turning effect depends on two things: how hard you push, and where you push.
The moment of a force equals the product of the magnitude of the force and the perpendicular distance of the line of action of the force from the axis of rotation.
Or, τ = F × d, where τ is the moment of force, F is the force in newtons, and d is the perpendicular distance in metres. Note that the S.I. unit N m is not written as joule, since torque is a vector while energy is a scalar. The S.I. unit is the newton-metre, written as N m. These units are related as 1 N m = 10⁷ dyne cm. The C.G.S. unit is the dyne centimetre, written as dyne cm.
Here is a practical example. Imagine a mechanic using a spanner to loosen a nut. If he applies 150 N of force at the end of a 40 cm handle, the moment is 150 times 0.4, which equals 60 N m. To achieve the same turning effect with only 50 N, he would need a handle 1.2 m long. This is why long-handled tools make work easier — they trade force for distance.
Moments have direction. By convention, anticlockwise moments are taken as positive, while clockwise moments are taken as negative. You can change the direction of rotation either by reversing the direction of your push, or by applying the same force on the opposite side of the pivot. A steering wheel demonstrates this beautifully — push down on the left rim, and the wheel turns one way; push down on the right rim with the same force, and it turns the opposite way.
When two equal and opposite forces act on a body at different points, they form what we call a couple. A couple produces rotation without translation, since the resultant force is zero but the resultant moment is not zero. The moment of a couple equals one force multiplied by the perpendicular distance between the two forces — this distance is called the couple arm.
So, moment of couple = F × d. Or, τ = F × d, where τ is the moment of couple, F is either force, and d is the couple arm.
Everyday examples abound: turning a water tap, winding a clock with a key, or pushing bicycle pedals. In each case, two forces work together, separated by a distance, to create rotation.
Let us now consider equilibrium — that delicate state where a body preserves its condition despite multiple forces acting upon it. Static equilibrium occurs when a body remains in a state of rest under the influence of several forces. A book lying on a table, its weight balanced by the upward reaction force of the table, is in static equilibrium. A balanced beam scale, with equal moments on either side, similarly rests in static equilibrium.
Dynamic equilibrium occurs when a body remains in the same state of motion, translational or rotational, under the influence of several forces. A raindrop falling at constant velocity, an aeroplane cruising at fixed altitude, or a planet orbiting the sun — all maintain their motion because the forces upon them balance out.
For any body to be in complete equilibrium, two conditions must be satisfied. First, the resultant of all the forces acting on the body should be zero — this ensures no change in translational motion. Second, the algebraic sum of moments of all the forces acting on the body about the point of rotation should be zero — this ensures no change in rotational motion.
This leads us to the principle of moments.
When a body is in equilibrium, the sum of anticlockwise moments equals the sum of clockwise moments about any point. A physical balance, or beam balance, operates on this very principle.
Picture a metre rule suspended horizontally by a thread at its centre. Hang weights from spring balances on either side. Adjust their positions until the rule lies perfectly horizontal. You will discover that weight multiplied by distance on one side precisely equals weight multiplied by distance on the other. This experimental verification confirms the principle of moments.
Now we turn to the centre of gravity — that special point where we can consider the entire weight of a body to act.
For any body, imagine it composed of countless tiny particles, each pulled downward by gravity. The centre of gravity is the point about which the algebraic sum of moments of weights of all the particles constituting the body is zero.
The position of the centre of gravity depends entirely on how mass is distributed within the body. A straight uniform rod balances at its midpoint. Bend that same rod into a circle, and its centre of gravity shifts to the geometric centre — a point that contains no material at all. This reveals an important truth: the centre of gravity need not lie within the physical substance of the body.
For regular shapes, we can predict the centre of gravity precisely. A hollow cone has its centre of gravity at a height of one-third the total height from the base. A solid cone has its centre of gravity at a height of one-quarter the total height from the base, on its axis. A circular disc or solid sphere — at the geometric centre. A cylinder — at the midpoint of its axis. A triangular lamina — at the intersection of its medians. A rectangle or parallelogram — where the diagonals cross.
For irregular shapes, we find it experimentally. When a body is freely suspended from a point, it comes to rest with its centre of gravity lying vertically below the point of suspension. Suspend the lamina from three different points, each time marking the vertical line indicated by a plumb line. Where these three lines intersect — that is your centre of gravity.
Finally, we arrive at uniform circular motion — motion along a circular path at constant speed.
Here lies a profound paradox: the speed never changes, yet the motion is accelerated. How can this be?
The answer lies in velocity. Velocity is a vector — it has both magnitude and direction. In circular motion, while speed remains constant, direction changes continuously. At every instant, the velocity points along the tangent to the circle at that point. North becomes west, west becomes south, south becomes east — the direction perpetually shifts. This continuous change in velocity means acceleration exists.
This acceleration requires a force — the centripetal force.
Always directed toward the centre of the circle, this force continuously pulls the body inward, preventing it from flying off in a straight line tangent to the path. Its magnitude equals mass times velocity squared divided by radius.
Or, F = mv²/r, where F is the centripetal force, m is mass, v is velocity, and r is the radius. The S.I. unit is the newton, since m²/s² divided by m gives m/s², and mass times acceleration gives force.
Examples surround us.
The word centripetal means centre-seeking. The electrostatic attraction between nucleus and electron keeps electrons in atomic orbits. Gravitational attraction binds planets to the sun and moons to planets. The tension in a string keeps a whirling stone in circular motion. Remove the centripetal force, and the body flies off along the tangent.
Now, a word of caution about centrifugal force.
You may have heard of it — a force seeming to push outward when you ride a merry-go-round or take a sharp turn in a car. But understand this: centrifugal force is not a real force. It is a fictitious force, perceived only by an observer rotating with the system.
Consider a ball tied to the centre of a rotating platform. An outside observer sees the ball pulled inward by string tension — the real centripetal force causing circular motion. But someone standing on the rotating platform sees the ball at rest beside them. To explain this, they must imagine a force balancing the tension — this imagined outward force is what we call centrifugal force. It is a fictitious force assumed by an observer moving in a circular path along with the body, not a real force.
Let us gather what we have learned. First, forces produce either translational or rotational motion, depending on whether the body is free to move or pivoted at a point. Second, the moment of force, or torque, depends on both force magnitude and perpendicular distance from the axis. Third, equilibrium requires both zero net force and zero net moment. Fourth, the centre of gravity is the point where the entire weight of the body can be considered to act. Fifth, uniform circular motion involves constant speed but changing velocity, requiring real centripetal force directed toward the centre of the circular path. And sixth, centrifugal force is fictitious — a fictitious force assumed by an observer moving with the body, not a real physical force.
Physics reveals the hidden patterns beneath everyday experience. The door you open, the bicycle you pedal, the moon that circles Earth — all obey these principles of force and motion. Carry this understanding forward, and you will see the world with new eyes.
Until our next lesson, keep questioning, keep observing, and keep thinking like a physicist. Goodbye for now.