Physics notes on Motion for competitive exams

Motion

Scalar Quantities: 

 Physical quantities which have magnitude only and no direction are called scalar quantities.
Example: Mass, speed, volume, work, time, power, energy etc.

Vector Quantities: 

Physical quantities which have magnitude and direction both and which obey triangle law are called vector quantities.
Example: Displacement, velocity, acceleration, force, momentum, torque etc.
Electric current, though has a direction, is a scalar quantity because it does not obey triangle law.
Moment of inertia, pressure, refractive index, stress are tensor quantities.

Distance: 

Distance is the actual path traveled  by a body in a given period of time.

Displacement:

• The change in the position of the object in a given period of time
•  Distance is a scalar quantity whereas displacement is a vector quantity both having the same unit (metre)
•  Displacement may be positive, negative or zero whereas distance is always positive.

Speed:

• Distance travelled by the moving object in unit time interval is called speed i.e. speed = Distance/ Time
• It is a scalar quantity and its SI unit is metre/second (m/s).
• Speed of an object at any instant is called instantaneous speed.
• An object is said to be traveled with non-uniform speed if it covers unequal distance in equal interval of time.

Velocity:

•  Velocity of a moving object is defined as the displacement of the object in unit time interval i.e., velocity =
• It is a vector quantity and its SI unit is metre/second.
• If a body goes equal displacement in equal interval of time then it is called uniform velocity.
• If a body undergoes unequal displacement in equal interval of time then it is called variable velocity.

Relative velocity
= V₁ +V₂ if two travels in opposite direction
=V₁-V₂ if two travels in same direction

Acceleration:

• Acceleration of an object is defined as the rate of change of velocity of the object .
• It is a vector quantity and its SI units is metre/second² (m/s²)
• If velocity decreases with time then acceleration is negative and is called retardation.
• If acceleration does not change with time it is called constant acceleration.
• Some equation of acceleration;

          V=u+at
         S=ut+at²/2
        V²= u²+2as
Here v=final velocity, u is initial velocity, t is time ineterval, a is acceleration and s is the distance travel.

Circular Motion:

• The motion of an object along a circular path it is called circular motion.
• If the object moves with uniform speed, its motion is uniform circular motion.
• Uniform circular motion is an accelerated motion because the direction of velocity changes continuously.

Angular Displacement and Velocity:

The angle subtended at the centre of a circle by a body moving along the circumference of the circle is called angular displacement of the body. It unit is radian.
Angular displacement= length of arc/radius of circle
Time rate of change of angular displacement is called angular velocity.
It is generally denoted by ω and 

Force:

• Force is that external cause which when acts on a body changes or tries to change the initial state of the body.
• Its SI unit is Newton(N).
• A body is said to be in equilibrium if the sum of all the forces acts on the body is Zero.
• Nuclear force is the strongest force.

Momentum:

•  Momentum is the property of a moving body and is defined as the product of mass and velocity of the body i.e.
•           Momentum = mass x velocity.
• It is a vector quantity. Its SI unit is kgm/s.

Newton’s Law:

Newton first law

If no external force acts on a body then it remains in the same state of rest or motion that is in its present state.

Inertia of Rest:

• Inertia is the property of a body by virtue of which it opposes any change in its state of rest or of uniform motion.
• When a bus or train at rest starts to move suddenly the passengers sitting in it feels jerk in backward direction due to inertia of rest.
• Dust particle come out of a carpet if we beat it with stick.
• A passenger jumping out of a train is advised to jump in the direction of bus and ran for a short distance.

Inertia of Motion:

When a running bus or train stops suddenly, the passengers sitting in it jerk in forward direction due to inertia of motion.

Newton's second law of motion:

• The rate of change in momentum of a body is directly proportional to the applied force on the body and takes place in the direction of force.

If F = force applied, a = acceleration produced and m = mass of body
then F = ma.

Newton's Third Law of Motion : 

To every action, there is an equal and opposite reaction.
Examples of third law –

• Recoil of a gun
• Motion of rocket
• While drawing water from the well, if the string breaks up the man drawing water falls back.

Centripetal Force:
When a body is in circular motion, a force always acts on the body towards the centre of the circular path, this force is called centripiatl force
If a body of mass m is moving on a circular path of radius R with uniform speed v, then the required centripetal force

Centrifugal Force:

• Centrifugal force is such a pseudo force.
• It is equal and opposite to centripetal force.

Application of centripetal and Centrifugal forces:

• Roads are banked at turns to provide required centripetal force for taking a turm.
• Cream is separated form milk when it is rotated in a vessel about the same axis.
• Gravitational force of attraction between earth and sun acts as centripetal force.
• Orbital motion of electrons around the nucleus
• Cyclist inclined itself from vertical to obtain required centripetal force.

Principle of conservation of linear momentum:

• If no external force acts on a system of bodies, the total linear momentum of the system of bodies remains constant.
• As a consequence, the total momentum of bodies before and after collision remains the same.
• As in case of rocket, ejecting gas exerts a forward force which helps in accelerating the rocket in forward direction.

Impulse:

• When a large force acts on a body for very small time, then force is called impulsive force.
• Impulse is defined as the product of force and time.
• Impulse = force x time = change in momentum.
• It is a vector quantity and its direction is the direction of force. Its SI unit is newton second (Ns).

Friction:

It is force which acts on a body when two body are in contact and one tries to move over other.
Types of Friction:
Static Friction:
The opposing force which acts on acts on a body when it tries to move over the other but actual motion has yet not started.
Limiting friction:
It is the force that comes to play, when a body is at the verge of moving over the other body.
Kinetic Friction:
This is the opposing force that comes to play when one body actually moves over the surface of another body is called kinetic friction. It is of two types which are as follows:
Sliding Friction: When a body slides over the surface of other
Rolling Friction: When a body rolls over the surface of another body

• It is easier to roll a body than to slide because the sliding friction is greater than the rolling friction.
• It is easy to drive a bicycle when its  tyres are fully inflated because it decreases rolling friction.

Application of Friction:

• A ball bearing is used to reduce the rotational friction.
• Friction is necessary for walking and to apply breaks in vehicles.
• When a pedal is applied to a bicycle, the force of friction on rear wheel is in forward direction and on front wheel it is in the backward direction.
• Friction can be reduced by applying the polishing or applying any lubricants.
• The tyre are made up of synthetic rubber because its coefficient of friction with road is larger and stops sliding the bicycle.