Here we are providing the short notes on Physics which will be help to crack science part in may examinations like SSC, Railway and other competitive exams.

# KINEMATICS

Table of Contents

**Kinematics**

Kinematics is branch of

**Kinematics**

Kinematics is branch of mechanics which deals with the study of motion of the objects without taking into account the cause of their motion.

**Rest and Motion**

An object is said to be at rest if it does not change its position which respect to its surroundings with time and said to be in **motion** if it changes its position with respect to its surrounding with time.

**Rectilinear motion**moving car on horizontal road, motion under gravity etc.**Angular****motion**such as particle going on a circle, projectile motion, rotation of machine shaft etc.**Rotational motion**such as motion of a fan.- It an object travels equal distances in equal intervals of time, then it is said to be in
**uniform motion.** - It an object travels unequal distances in equal intervals of time, then it is said to be in
**non-uniform motion.**

**Speed**

- The distance covered by a moving body in a unit time interval is called its speed.
- Speed =
- When a body travels equal distances with speed and , then average speed is the
**harmonic mean**of the two speeds. - When a body travels for equal times with speeds and , then average speed is the
**arithmetic mean**of the two speeds.

**Velocity**

- The time rate of change of displacement of a body is called its velocity.
- An object is said to be moving with
**uniform velocity**if it undergoes equal displacements in equal intervals of time. - An object is said to be moving with
**non-uniform**or**variable velocity**if it undergoes unequal displacement in equal intervals of time. - Average velocity =

**Acceleration**

- The time rate of change of velocity of a body is called its acceleration.
- Acceleration =
- It is a vector quantity and its SI unit is .
- Acceleration at an instant of time is known as
**instantaneous acceleration.** - When the velocity of a body increases with time, then its acceleration is positive and if velocity decreases with time, then its acceleration is negative called
**deceleration or retardation.** - If acceleration does not change with time, it is said to be
**constant acceleration.**

**Equations of Uniformly Accelerated Motion** (Along straight line)

If a body started its motion with initial velocity u and attains final velocity v in the interval t. The acceleration assumed to be uniform in motion is a and the distance travelled is s, then equations of motion:

- If any body is falling freely under gravity, then a is replaced by g in above equations.
- If an object is thrown vertically upward, then in above equations of motion a is replaced by (–g).
- For a body with zero acceleration or constant speed, graph between velocity and time will be a line parallel to time axis.
- Velocity–Time Graph For accelerating or decelerating body the graph will be a straight line inclined to time axis and velocity axis.
- Graph between position (distance)-time for an accelerating or decelerating body is always a parabola.
- Acceleration-time graph for uniformly accelerating body is a line parallel to time axis.
- In case of uniform accelerated, the graph between position and velocity is always parabola.
- In case of uniformly accelerated motion, the graph between velocity and time is always a straight line.
- Slope of displacement-time graph gives velocity and slope of velocity-time graph gives acceleration.

**Projectile Motion**

- When a body is thrown from horizontal making an angle (θ) except 90°, then its motion under gravity is a curved parabolic path, called trajectory and its motion is called projectile motion.

Examples:

- The motion of a bullet shot from the gun
- The motion of a rocket after burn-out
- The motion of a bomb dropped from a aeroplane etc.

**Properties of Projectile Motion**

If we drop a ball from a height and at the same time thrown another ball in a horizontal direction, then both the balls would strike the earth simultaneously at different places.

**Circular Motion**

- The motion of an object along a circular path is called circular motion.
- Circular motion with a constant speed is called
**uniform circular motion.** - The direction of motion at any point in circular motion is given by the tangent to the circle at that point.
- In uniform circular motion, the velocity and acceleration both changes.
- In case of non-uniform circular motion, the speed changes from point to point on the circular track.

**Centripetal Acceleration**

During circular motion an acceleration acts on the body towards the centre, called centripetal acceleration.

The direction of centripetal acceleration is always towards the centre of the circular path.

**Force**

It is an external push or pull with can change or tries to change the state of rest or of uniform motion. SI unit is newton (N) and CGS unit is dyne. 1 N = dyne.

If sum of all the forces acting on a body is zero, then body is said to be in equilibrium.

**Centripetal Force**

During circular motion a force always acts on the body towards the centre of the circular path, called centripetal force.

**Centrifugal Force**

In circular motion we experience that a force is acting on us in opposite to the direction of centripetal force called **centrifugal force.** This is an apparent force or imaginary force and also called a pseudo force.

**Applications of centripetal and centrifugal forces**

- Cyclist inclined itself from vertical to obtain required centripetal force. To take a safe turn cyclist slower down his speed and moves on a path of larger radius.
- Roads are banked at turns to provide required centripetal force for taking a turn.
- For taking turn on a curved road, the
**frictional force**is acting between the tyres of the vehicle and the road acts as centripetal force. - If a bucket containing water is revolved fast in a vertical plane, the water may not fall even when bucket is completely inverted because a centrifugal force equal or greater than the weight of water pushes the water to the bottom of the bucket.
- For orbital motion of electrons around the nucleus
**electrostatic force**of attraction is acting between the electrons and the nucleus as centripetal force. - Cream is separated from milk when it is rotated in a vessel about the same axis. During rotation lighter particles of cream experience a lesser force than the heavier particles of milk.
- For revolution of the earth around the sun, gravitational force of attraction between the earth and the sun acts as centripetal force.

mechanics which deals with the study of motion of the objects without taking into account the cause of their motion.

**Rest and Motion**

An object is said to be at rest if it does not change its position which respect to its surroundings with time and said to be in **motion** if it changes its position with respect to its surrounding with time.

**Rectilinear motion**moving car on horizontal road, motion under gravity etc.**Angular****motion**such as particle going on a circle, projectile motion, rotation of machine shaft etc.**Rotational motion**such as motion of a fan.- It an object travels equal distances in equal intervals of time, then it is said to be in
**uniform motion.** - It an object travels unequal distances in equal intervals of time, then it is said to be in
**non-uniform motion.**

**Speed**

- The distance covered by a moving body in a unit time interval is called its speed.
- Speed =
- When a body travels equal distances with speed and , then average speed is the
**harmonic mean**of the two speeds. - When a body travels for equal times with speeds and , then average speed is the
**arithmetic mean**of the two speeds.

**Velocity**

- The time rate of change of displacement of a body is called its velocity.
- An object is said to be moving with
**uniform velocity**if it undergoes equal displacements in equal intervals of time. - An object is said to be moving with
**non-uniform**or**variable velocity**if it undergoes unequal displacement in equal intervals of time. - Average velocity =

**Acceleration**

- The time rate of change of velocity of a body is called its acceleration.
- Acceleration =
- It is a vector quantity and its SI unit is .
- Acceleration at an instant of time is known as
**instantaneous acceleration.** - When the velocity of a body increases with time, then its acceleration is positive and if velocity decreases with time, then its acceleration is negative called
**deceleration or retardation.** - If acceleration does not change with time, it is said to be
**constant acceleration.**

**Equations of Uniformly Accelerated Motion** (Along straight line)

If a body started its motion with initial velocity u and attains final velocity v in the interval t. The acceleration assumed to be uniform in motion is a and the distance travelled is s, then equations of motion:

- If any body is falling freely under gravity, then a is replaced by g in above equations.
- If an object is thrown vertically upward, then in above equations of motion a is replaced by (–g).
- For a body with zero acceleration or constant speed, graph between velocity and time will be a line parallel to time axis.
- Velocity–Time Graph For accelerating or decelerating body the graph will be a straight line inclined to time axis and velocity axis.
- Graph between position (distance)-time for an accelerating or decelerating body is always a parabola.
- Acceleration-time graph for uniformly accelerating body is a line parallel to time axis.
- In case of uniform accelerated, the graph between position and velocity is always parabola.
- In case of uniformly accelerated motion, the graph between velocity and time is always a straight line.
- Slope of displacement-time graph gives velocity and slope of velocity-time graph gives acceleration.

**Projectile Motion**

- When a body is thrown from horizontal making an angle (θ) except 90°, then its motion under gravity is a curved parabolic path, called trajectory and its motion is called projectile motion.

Examples:

- The motion of a bullet shot from the gun
- The motion of a rocket after burn-out
- The motion of a bomb dropped from a aeroplane etc.

**Properties of Projectile Motion**

If we drop a ball from a height and at the same time thrown another ball in a horizontal direction, then both the balls would strike the earth simultaneously at different places.

**Circular Motion**

- The motion of an object along a circular path is called circular motion.
- Circular motion with a constant speed is called
**uniform circular motion.** - The direction of motion at any point in circular motion is given by the tangent to the circle at that point.
- In uniform circular motion, the velocity and acceleration both changes.
- In case of non-uniform circular motion, the speed changes from point to point on the circular track.

**Centripetal Acceleration**

During circular motion an acceleration acts on the body towards the centre, called centripetal acceleration.

The direction of centripetal acceleration is always towards the centre of the circular path.

**Force**

It is an external push or pull with can change or tries to change the state of rest or of uniform motion. SI unit is newton (N) and CGS unit is dyne. 1 N = dyne.

If sum of all the forces acting on a body is zero, then body is said to be in equilibrium.

**Centripetal Force**

During circular motion a force always acts on the body towards the centre of the circular path, called centripetal force.

**Centrifugal Force**

In circular motion we experience that a force is acting on us in opposite to the direction of centripetal force called **centrifugal force.** This is an apparent force or imaginary force and also called a pseudo force.

**Applications of centripetal and centrifugal forces**

- Cyclist inclined itself from vertical to obtain required centripetal force. To take a safe turn cyclist slower down his speed and moves on a path of larger radius.
- Roads are banked at turns to provide required centripetal force for taking a turn.
- For taking turn on a curved road, the
**frictional force**is acting between the tyres of the vehicle and the road acts as centripetal force. - If a bucket containing water is revolved fast in a vertical plane, the water may not fall even when bucket is completely inverted because a centrifugal force equal or greater than the weight of water pushes the water to the bottom of the bucket.
- For orbital motion of electrons around the nucleus
**electrostatic force**of attraction is acting between the electrons and the nucleus as centripetal force. - Cream is separated from milk when it is rotated in a vessel about the same axis. During rotation lighter particles of cream experience a lesser force than the heavier particles of milk.
- For revolution of the earth around the sun, gravitational force of attraction between the earth and the sun acts as centripetal force.