9th Class Science Time and Motion Motion

Motion

In the physical world, one of the most common phenomena is motion. The branch of Physics, which deals with the behavior of moving objects, is known as mechanics. Mechanics is further divided into two sections namely Kinematics and Dynamics.

Kinematics deals with the study of motion without taking into account the cause of 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 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.

Distance: Distance is the length of actual path covered by a moving object in a given time interval.

Displacement: Shortest distance covered by a body in a definite direction is called displacement.

Distance is a scalar quantity whereas displacement is a vector quantity both having the same unit.

Displacement may be positive, negative or zero where distance is always positive,

Speed: Distance travelled by the moving object in unit time interval is called speed

Speed = Distance/Time. It is a scalar quantity and its SI unit is meter/second.

Velocity: Velocity of a moving object is defined as the displacement of the object in unit time interval i.e. velocity = Displacement/Time.

It is vector quantity and its SI unit is meter/second.

Acceleration: Acceleration of an object is defined is the rate of change of velocity of the object. Acceleration = Change in velocity/Time.

It is a vector quantity and its SI unit is meter/\[{{\operatorname{second}}^{2}}\].

Circular Motion: It an object describes a circular path its motion 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 Motion: The angle subtended by the line joining the object from the origin of circle in unit time interval is called angular motion.

It is generally denoted by \[\omega \] and \[\omega ~=\theta /t\].

If T= time period = time taken by the object to complete one revolution,

n = frequency = no. of revolutions in one second.

nT = 1 and \[\omega =2\pi /T=2\pi n\].

In one revolution the object travels \[2\pi r\] distance.

Linear speed =\[\omega r=angular\text{ }speed\times radius\].

Newton’s Laws of Motion

Newton the father of physics established the laws of motion in his book ‘principia’ in 1667.

Newton's first laws of motion: Everybody maintains its initial state of rest or motion with uniform speed on a straight line unless an external force acts on it.

First law is also called law of Galileo or law of inertia.

Inertia: Inertia is the property of a body by virtue of which the body opposes change in its initial state of rest or motion with uniform speed on a straight line.

Inertia is of two types (1) Inertia of rest (2) Inertia of motion.

Example:

Force: Force is that external cause which when acts on a body changes or tries to change the initial state of the body.

Momentum: Momentum is the property of a moving body and is defined as the product of mass and velocity of the body. \[\operatorname{Momentum}=mass\times velocity.\]

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 the body, then F = ma.

Newton's Third laws of Motion: To every action there is an equal and opposite reaction.

Example:

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

Principal 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.

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.

\[\operatorname{Impulse} = force\times time = change in momentum\].

It is a vector quantity and its direction is the direction of force. Its SI unit is newton second (Ns).

Centripetal Force: When a body-travels along a circular path, its velocity changes continuously.

Naturally an external force always acts on the body towards the centre of the path.

The extemal force required to maintain the circular motion of the body is centripetal 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, \[\operatorname{F}=\frac{m{{v}^{2}}}{R}\].

Centre of Gravity: The centre of gravity of a body is that point through which the entire weight of body acts. The centre of gravity of a body does not change with the change in orientation of body in space.

The weight of a body acts through centre of gravity in the downward direction. Hence a body can be brought to equilibrium by applying a force equal to its weight in the vertically upward direction through centre of gravity.