Revision: Force, Work, Power and Energy >> Force Physics (English Medium) ICSE Class 10 CISCE

1 dyne is that force which when acting on a body of mass 1 gram, produces an acceleration of 1 cm s^-2 in it.
1 dyne = 1 g × 1 cm s^-2.

Force is defined as the rate of change of linear momentum of a body with respect to time.

An inclined plane is usually a smooth, flat rigid surface inclined at an angle (θ) to the horizontal. It is used to raise heavy loads with a relatively small force. The longer the slope, the smaller is the effort needed.

The forces which are applied on a body through a connector, are called contact forces. Forces like Frictional force, Mechanical force, etc., are the forces of contact.

Now consider a body pivoted at a point, i.e., not free to move, and a force is applied on the body at a suitable point, it rotates the body about the axis passing through the pivoted point. This is the turning effect of the force and the motion of the body is called rotational motion.

When a force acts on a stationary rigid body that is free to move, the body starts moving in a straight path in the direction of the applied force. This is called linear or translational motion.

The turning effect produced by a force on a rigid body about a point, pivot or fulcrum is called the moment of force or torque. It is measured by the product of force and the perpendicular distance of the pivot from the line of action of force.

Moment of a force = Force × perpendicular distance of the pivot from the force.

The turning effect of force acting on a body about an axis is called the moment of force.

Force is a physical cause that changes or may tend to change the state of rest or the state of motion of an object. 

The forces which act on a body without the help of any connector, are called non-contact forces or forces of distance. Gravitational force, Mechanical force, etc., are non-contact forces.

The physical quantity is ‘torque’.

Torque may be defined as the turning effect produced by a force on a rigid body about a point, pivot, or fulcrum. It is measured by the product of force and the perpendicular distance of the pivot from the line of action of force.

The moment of a force (or torque) is equal to 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. 

Two equal and opposite parallel forces, not acting along the same line, form a couple. A couple is always needed to produce a rotation.

The moment of a couple is equal to the product of either force and the perpendicular distance between the line of action of both the forces.

The perpendicular distance between the two forces is AB ( = d), which is called the couple arm.

The momentum of a body is the product of the mass of the body and its velocity, i.e. p = mv.

When a number of forces acting on a body produce no change in its state of rest or of linear or rotational motion, the body is said to be in a state of equilibrium.

When a body remains in a state of rest under the influence of several forces, the body is in static equilibrium.

When a body remains in the same state of motion (translational or rotational), under the influence of several forces, the body is said to be in dynamic equilibrium. 

The centre of gravity is an imaginary location where the body’s whole weight is assumed to be concentrated.

The Centre of Gravity (c.g.) of a body is the point around which the resultant torque due to the force of gravity on the body is zero.

or

The centre of gravity (C.G.) of a body is the point about which the algebraic sum of moments of the weights of all the particles constituting the body is zero. The entire weight of the body can be considered to act at this point, howsoever the body is placed.

OR

The point about which the resultant torque due to force of gravity on the body is zero is called the centre of gravity.

The component of acceleration directed towards the centre of the circular path is called centripetal acceleration (or radial acceleration).

When a particle moves with a constant speed in a circular path, its motion is said to be the uniform circular motion.

The force directed towards the centre along the radius, required to keep a body moving along a circular path at constant speed, is called centripetal force.

Angular velocity of a particle is the rate of change of angular displacement.

When a particle moves with a constant speed in a circular path, its motion is said to be uniform circular motion.

OR

The motion of a body moving with constant speed along a circular path is called uniform circular motion.

OR

The motion of a body moving with constant speed along a circular path, where the velocity is always tangential to the circular path and remains constant in magnitude, is called uniform circular motion.

The angle traced out by the radius vector at the centre of the circular path in a given time, expressed as Δθ = θ₂ − θ₁​, is called angular displacement.

The rate of change of angular displacement of a body undergoing circular motion is called angular velocity.

The rate of change of angular velocity of a body is called angular acceleration.

Centripetal force is the force acting on a body moving in a circular path, in a direction towards the centre of the circular path.

OR

A force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force.

OR

The inward force required to keep an object moving in a circular path, directed towards the centre of the circle, expressed as F_C = \[\frac {mv^2}{r}\] = mrω², which always acts perpendicular to the direction of linear velocity, is called Centripetal Force.

At each of circular path, the particle, instead of moving straight continuously, turn towards the centre. Therefore, the motion in the circular path is under the action of a force called the centripetal force.

A force assumed (by an observer moving with the body) to be acting on the body in a direction away from the centre of a circular path is called centrifugal force. 

A force which really does not exist, but is considered to describe (or understand) a certain motion, is called a fictitious force (or virtual force). 

\[\overset{\rightarrow}{\operatorname*{F}}=\frac{d\overset{\rightarrow}{\operatorname*{p}}}{dt}=\frac{d(m\overset{\rightarrow}{\operatorname*{v}})}{dt}\]

or

\[\begin{array}
{rcl}\vec{F} & = & m\vec{a}
\end{array}\](if mass m is constant)

Moment of force = Force × perpendicular distance from the point (axis) of rotation

τ =  F × d

Moment of Couple = Either force x perpendicular distance between the two forces (or couple arm) 

\[F_C=\frac{mv^2}{r}=mr\omega^2=mv\omega\quad(v=r\omega)\]

• Force is a Vector Quantity
• Unit of Force is Newton (symbol N) or kilogram-force (symbol kgf), where 1 kgf = g N if g is the acceleration due to gravity at that place (= 9·8 m s^-2 average value on the earth's surface). 

• A force applied to a pivoted body causes rotation (not linear motion) about the axis passing through the pivot point.
• The turning effect of a force (torque) depends on two factors:
  The magnitude of the force
  The perpendicular distance from the axis of rotation
• Maximum torque is produced when the force is applied at the maximum perpendicular distance from the axis.
• The S.I. unit of moment of force is newton-metre (N·m), and the C.G.S. unit is dyne-centimetre.
• Anticlockwise moments are taken as positive and directed outwards from the axis, while clockwise moments are negative and directed inwards.

Conditions for Equilibrium of Bodies:

1. The resultant of all the forces is zero, so they do not change either the state of rest or the state of linear motion of the body, and
2. The algebraic sum of moments of all the forces about the fixed point is zero, so they do not change the rotational state of the body.

• The weight of a body acts through a single point called the centre of gravity (C.G.), where the sum of moments of all particles' weights is zero.
• The position of the C.G. depends on the shape and mass distribution of the body and changes if the body is deformed.
• The C.G. may lie outside the material of the body (e.g., a ring or hollow sphere).
• A body balances when supported exactly at its centre of gravity, as seen in a metre rule or square lamina.
• The C.G. of an irregular lamina can be found by suspending it from multiple points and tracing the intersection of plumb line paths.

• In UCM, speed is constant, but velocity continuously changes direction, always remaining tangential to the path.
• Angular displacement is the angle swept by the radius vector; angular velocity is its rate of change.
• Even at constant speed, centripetal acceleration is never zero — it always acts towards the centre of the circular path.
• Centripetal force is always directed towards the centre and is essential to maintain circular motion — it does no work on the body.
• If speed is constant in circular motion, tangential acceleration = 0, but radial acceleration ≠ 0.