KINEMATICS

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.

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·         When a body travels for equal times with speeds  and , then average speed is the arithmetic mean of the two speeds.

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Velocity

·         The time rate of change of displacement of a body is called its velocity.

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·         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:

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·         

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·         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.

Newton’s Laws

Newton’s First Law

A body continues in its state of rest or of uniform motion in a straight line unless an external force acts on it. It is based on

law of inertia.

Inertia is the property of a body by virtue of which is opposes any change in its state of rest or of uniform motion in a straight line.

Inertia of Rest

·         When a bus or train at rest starts, to move suddenly, the passangers sitting in it jerk in backward direction due to their inertia of rest.

·         The dust particles come out from a carpet when it is beaten with a stick due to their inertia of rest.

·         A passenger jumping out from a rapidly moving bus or train is advised to jump in forward direction and run forward for a short mile due to inertia of rest.

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

Momentum

The momentum of a moving body is equal to the product of its mass and its velocity.

Conservation of Linear Momentum

The linear momentum of a system of particles remains conserved if the external force acting on the system is zero.

·         Rocket propulsion and engine of jet aeroplane works on principle of conservation of linear momentum. In rocket, ejecting gas exerts a forward force which helps in accelerating the rocket upward.

Newton’s Second Law

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

Newton’s Third Law

For every action, there is an equal and opposite reaction and both act on two interacting objects.

Rocket is propelled by the principle of Newton’s third law of motion.

Impulse

·         A large force which acts on a body for a very short interval of time and produces a large change in its momentum is called an impulsive force.

·         Its unit is newton-second.

·         A fielder lowers its hand when catching a cricket ball because by lowering his hands, he increases the time of contact for stopping the ball and therefore fielder has to apply lesser force to stop the ball. The ball will also exert lesser force on the hands of the fielder and the fielder will not get hurt.

·         Wagons of a train are provided with the buffers to increase the time of impact during jerks and therefore, decreases the damage. The vehicles like scooter, car, bus, truck etc. are provided with shockers.

Friction

Friction is a force which opposes the relative motion of the two bodies when one body actually moves or tries to move over the surface of another body.

The cause of friction is the strong atomic or molecular forces of attraction acting on the two surfaces at the point of actual contact.

Uses of Friction

·         A ball bearing is a type of rolling-element that uses balls to maintain the separation between the bearing races. The purpose of a ball bearing is to reduce rotational friction and to support loads (weight).

·         Friction is necessary for walking, to apply brakes in vehicles, for holding nuts and bolts in a machinery etc.

·         Friction can be decreases by polishing the surfaces by using lubricants or by using ball bearings.

·         Tyres are made of synthetic rubber because its coefficient or friction with road is larger and therefore, large force of friction acts on it, which stops sliding at turns.

·         The tyres are threading which also increases the friction between the tyres and the road.

·         When pedal is applied to a bicycle, the force of friction on rear wheel is in forward direction and on front wheel is in the backward direction.

Loses due to Friction

·         Too much Loss of Energy in machines and then ultimately the machines are damaged.

Machine–Lever

It is a simple machine in which a straight or inclined rod is made to turn or rotate at a point freely or independently. There are three points related to lever namely load, effort and fulcrum.

·         Load The weight carried by the lever is called load.

·         Effort To operate lever, the force applied externally is called effort.

·         Fulcrum The fixed point about which the rod of lever moves independently is called fulcrum.