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

• 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.

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.

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

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

“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.

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.

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.

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.

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.

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 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.

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

The time taken by a particle performing uniform circular motion to complete one revolution is called time period.

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.

"If no force is acting on a body, its velocity does not change, i.e., the body does not accelerate. In other words, if a body is stationary, it will remain stationary. If it is in motion, it will continue moving with the same velocity and in the same direction."

or

"An object continues to remain at rest or in a state of uniform motion along a straight line unless an external unbalanced force acts on it."

or

"Every inanimate object continues to be in its state of rest or of uniform unaccelerated motion unless and until it is acted upon by an external, unbalanced force."

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.

"The rate of change of momentum is proportional to the applied force, and the change of momentum occurs in the direction of the force."

"Every action force has an equal and opposite reaction force which acts simultaneously."

The concise law statement is: "To every action (force), there is an equal and opposite reaction (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\[\vec v\]

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

• 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.