Revision: Laws of Motion Science SSC (English Medium) 9th Standard Maharashtra State Board

The length of path travelled by a body in certain interval of time is called distance.

Displacement of an object between two points is the shortest distance between these two points.
“It is the unique path that can take the body from its initial to the final position.”

The displacement of a moving body is defined as the change in its position along a particular direction

• Displacement is the shortest distance in a straight line between the starting point and the final point, along with a direction. It is a vector quantity, meaning it includes both magnitude (distance) and direction.
• Example: In Ranjit’s case, the displacement is the straight line AD from his house to the school.

• Distance is the total length of the path travelled by a moving object, regardless of the direction. It is a scalar quantity, which means it only has magnitude (size), not direction.
• Example: If Ranjit walks from point A to B to C to D, the distance is the total of AB + BC + CD.

Speed is the distance travelled by an object in a given amount of time without considering the direction.

Formula: Speed = `"Distance traversed" / "Total time."`​

Non-uniform motion is used to mean the movement in which the object does not cover the same distance in the same distances in the same time intervals, regardless of the length of the time intervals. Every time the speed of the moving object changes by a different proportion at the same time interval, the motion of the body is observed as non-uniform motion.

For example:

1. A horse running.
2. A bouncy ball.
3. A car coming to a halt.

“In physics, uniform motion is defined as the motion where the velocity of the body travelling in a straight line remains the same. When the distance travelled by a moving thing is the same at several time intervals, regardless of the time length, the motion is said to be uniform motion.”

For example,

• The hour hand of the clock: It moves with uniform speed, completing movement of a specific distance in an hour.
• An aeroplane is cruising at a level height and a steady speed.
• A car is going along a straight, level road at a steady speed.

Negative acceleration or deceleration or retardation:
If the velocity of an object decreases with respect to time, then the object is said to be in negative acceleration or deceleration, or retardation.

Positive acceleration:
If the velocity of an object increases with respect to time, then the object is said to be in positive acceleration or just acceleration.

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

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.

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

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.

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.

Newton’s second law of motion states that the rate of change of momentum is directly proportional to force applied and takes place in the direction of the force.

\[\vec F\] = m \[\frac{d\vec{\mathrm{v}}}{dt}\] = m\[\vec a\] ... (for constant mass)

Thus, if \[\vec F\] = 0, \[\vec v\] is constant. Hence, if there is no force, velocity will not change. This is nothing but Newton's first law of motion.

General Form: \[\vec F\] =\[\frac{d\vec{p}}{dt}\]

For Constant Mass: \[\vec F\] = m\[\vec a\]

Momentum: \[\vec p\] = m\[\vec v\]

\[\vec{F}=\frac{d\vec{p}}{dt}=\frac{d\left(m\vec{\mathrm{v}}\right)}{dt}\]

Statement:

Every inanimate object continues to be in a state of rest or of uniform unaccelerated motion along a straight line, unless it is acted upon by an external, unbalanced force.

Importance:

• It shows the equivalence between the state of rest and the state of uniform motion along a straight line — the distinction lies only in the choice of frame of reference.
• It defines force as a physical entity that brings about a change in the state of motion or rest of an object.
• It defines inertia as a fundamental and inherent property of every physical body by virtue of which it resists any change in its state of rest or uniform motion along a straight line.

Statement:

The rate of change of linear momentum of a rigid body is directly proportional to the applied (external unbalanced) force and takes place in the direction of force.

F = Δp = m\[\frac {dv}{dt}\] = ma

Importance:

• It provides a mathematical formulation for the quantitative measure of force: F = \[\frac {Δp}{Δt}\] = ma.
• It defines momentum as the product of mass and velocity: p = mv.
• Aristotle's fallacy is overcome by establishing that it is the resultant unbalanced force — not force itself — that is required to maintain a change in the state of motion.

Statement:

To every action (force) there is always an equal and opposite reaction (force).

Importance:

• It defines action and reaction as a pair of equal and opposite forces acting along the same line — whenever one object exerts a force on another, the second object exerts an equal and opposite force on the first.
• Action and reaction forces always act on different objects and therefore never cancel each other out.

• 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.