Motion - Laws of Motion, Types and Examples

If the position of an object in space changes with time relative to an observer, it is said to be in motion. Motion occurs when an object change its location in space. Motion is a relative rather than an absolute term. An object may be in motion with regard to another object, but may be stationary with respect to a third object. For example, suppose you are riding on a train and you pass a person standing alongside the tracks. The person standing along the tracks will see you and everyone else on the train as being in motion. But the person sitting next to you on the train will be stationary with respect to you. Everything in the universe is in motion. Even as you sit reading a book, you are moving very rapidly because the earth is rotating its axis. You are also moving with the earth as it revolves around the sun. In addition, the sun, the earth and the rest of the planets in our solar system are involved in the general rotation of our galaxy within the universe.

We cannot imagine a state of motionlessness. Force and motion are related to each other like two sides of a coin. If any object is moving, there is definitely a force behind it. What if we want to make a moving object stand still? A force will have to be applied there too. The motion of objects is the most common phenomenon in nature. All physical phenomena are related to motion. The scientific basis for the study of motion was provided by scientists such as Galileo, Kepler and Newton. The laws which govern the motion of bodies were discovered by the scientist Sir Issac Newton.

Physical Quantities

Physical Quantities are of two types – Scalar and Vector Quantities. Scalar Quantities have only magnitude and no direction. For Example - Distance, Mass, Temperature, Speed etc. Vector Quantities have both magnitude and direction. For Example – Displacement, Weight, Velocity, Acceleration etc.

Distance and Displacement

The actual length of path travelled by a body is called the distance covered by a body. The shortest distance from the initial to the final position of a body is called displacement of the body. It does not depend on the actual path undertaken by the object. It has a direction and a magnitude. Its unit is the meter (m). When describing displacement, it is complete only if the direction is also indicated along with the distance traveled. Physical quantities that require a direction along with a magnitude are called vector quantities. Physical quantities that do not require a direction are called scalar quantities. Like ordinary numbers, vectors can be added, subtracted, multiplied, and divided. When an object moves in the same direction along a straight line, its distance and displacement are equal.

Speed and Velocity

The rate of change in position of objects when a force is applied is called speed. If this change in position occurs in a particular direction, it is called velocity. As a ball thrown into the sky falls, its velocity increases. This happens because the gravitational force of the Earth continuously acts on it.

Speed: Speed ​​is the distance travelled by a body in unit time. It is a scalar quantity. The basic SI unit of speed is meters/second or kilometers/hour.

Speed ​​= distance travelled by the object/time travelled by the object

If an object travels equal distances in equal interval of time, its movement is at the same speed. It is called uniform speed. If the object travelled different distance in equal (similar) time intervals then it is referred to as non-uniform speed. A speedometer is an instrument that measures the speed of a vehicle.

Velocity : Velocity is the displacement per unit time. Velocity is the rate at which a body moves in space in a given direction. Velocity is expressed in distance and time, such as metres per second. The distinction between velocity and speed is significant. Although it doesn't provide anything about the direction of motion, speed does reveal the rate of motion. When a body is said to have a speed of 40 kms per hour, the direction is unknown. To specify the velocity, it is necessary to indicate both the rate and the direction of motion. For example, a body may have a velocity of 40 kms per hour toward the north. Mathematically, velocity is a vector quantity, because it has both speed and direction.

The basic SI unit of velocity is - meter/second or kilometer/hour.

Velocity = displacement/total time taken to travel

When the amount of displacement of an object is equal at equal intervals and is moving in the same direction, the velocity of that object is uniform. If the direction and speed of an object are changing, the velocity of that object is non uniform.

Acceleration and Retardation

Acceleration

Acceleration is the rate of change of velocity. It is a vector quantity. Imagine a stone tied to a string spinning in a circle. Although the speed is the same, the direction of the stone changes every moment. As the direction changes, the velocity also changes. The change in the velocity of an object in a given time is called acceleration. The scientist who proposed the concept of acceleration was Galileo Galilei. Acceleration is the change in velocity per unit time. That is, the term acceleration refers to the increase in velocity. The basic unit of acceleration is meters/second squared. Acceleration is a vector quantity.

Acceleration = Change in Velocity/Time = (v - u) / t

v = final velocity, u = initial velocity, t = time interval

If the acceleration remains constant, i.e, it does not change with time it is said to be uniform acceleration.

Retardation

A decrease in the velocity with time is called deacceleration or retardation. If the acceleration is negative, it is called deceleration or negative acceleration.

Projectile and Trajectory

Projectile is the name given to a body which after having been given an initial velocity is allowed to move under the influence of gravity alone. The path of the projectile is called trajectory. The trajectory of a projectile moving under the influence of a constant acceleration is a parabola. A projectile has maximum range when the angle of projection is 45°.

Types of Motion

1. Linear Motion

If an object moves in a straight line, it is called Linear Motion. If this motion is at a constant speed, it is called Uniform Linear Motion. The object travels the same distance in a given time. Non-Uniform Linear Motion is linear motion that is not at a constant speed.

Example of Linear Motion - A mango falling suddenly

2. Circular Motion

Circular Motion is a motion in which different parts of a body move around a central fixed point or axis in a circular path with different radii. The movement of an object along a circular path is called 'Circular Motion'. The Earth's rotation around the Sun, the movement of a pencil when drawing a circle using a compass, the movement of a clock's needle, and the movement of a stone when a string is tied to it are all examples of circular motion.

3. Rotatory Motion

When an object moves, the centers of the circles drawn by each point on it lie on the same line. This line is the axis of the circle. Rotational motion is when an object rotates on its own axis.

Example: The earth rotating on its own axis, a rotating chair, a rotating drum, a small wheel in a sewing machine, wheels in a powder mill, the motion of a spinning wheel, the motion of the blades of a rotating fan

4. Revolutionary Motion

Orbit is the motion of a rotating object that is outside the axis of the object.

Example: The annual motion of the Earth around the Sun

5. Projectile Motion

When an object is thrown or launched and is in flight, it is called a projectile. A football, a cricket ball, or a baseball can all be projectiles. Projectile motion can be thought of as the result of two separate and simultaneous forces. The acceleration experienced by the object after launch is due to gravity. Moreover, it is experienced vertically downward. "The limits of projectiles known as two different slopes equal to or less than 45° are equal". The initial energy and, consequently, momentum of the launched projectile are lost due to forces such as friction, viscous force, and air resistance. Thus, the projectile travels a parabolic path and falls to the ground.

6. Translatory Motion

It is a motion in which every part of a body moves in the same direction by an equal distance at the same time. For Example – Moving vehicles like cars, buses, trains

7. Rectilinear Motion

It is a motion along a straight line. Example – The up and down movement of lifts.

8. Curvilinear Motion

Curvilinear Motion is a motion along a curved path. Example – The motion of a rocket in space.

9. Oscillatory Motion

It is a motion in which a body moves back and forth about its mean position. All vibratory motions are oscillations.

Examples: The motion of the pendulum in a pendulum clock, a simple pendulum, the motion of a hanging lamp, the motion of ocean water as ocean waves pass by, the movement of a swing.

10. Periodic Motion

It is a motion which repeats itself after a fixed interval of time. All oscillatory motions are periodic motions. Example – The rotation of the earth around the sun.

Dimensions of Motion

One Dimensional Motion – If the motion of an object is restricted to a straight line, it is an one dimensional motion. Example – Train running along a straight track.

Two Dimensional Motion – If the motion of an object is restricted to a plane, it is a two dimensional motion. Example – motion of a boat on a lake, a coin along a surface, motion of projectiles, motion of satellites, motion of charged particles in electric and magnetic fields.

Three Dimensional Motion – An object moving in space is said to be in three dimensional motion. Example – A butterfly flying in air or motion of gas molecules in space.

Momentum

Momentum is defined as the product of mass and velocity of a body. In physics, Newton defined momentum as a moving body's amount of motion. When a cricket bat is swung, it has a momentum that depends on its mass and how fast it moves. The force exerted on the ball when the ball hits it depends on the rate of change in the bat's momentum. Any moving object's momentum can be calculated by multiplying its mass by its velocity.  If a car has a mass of 1000 kilograms, when driving north at 5 metres per second, it has a momentum of 5000 kgm metres per second toward the north. To have the same momentum as the car, the truck having mass of 5000 kilograms, must drive north at only 1 metre per second. Momentum is a vector quantity.

If Mass = 'm' and velocity = 'v'

Then, Momentum = Mass x Velocity, i.e, P = mv

Unit of Momentum = kgm/s

Inertia

Inertia is the tendency of a body to continue in its state of rest or the state of uniform motion along a straight line. Inertia is a property of all matter. It makes an object that is not moving continue motionless unless some force puts it into motion. Inertia also makes a moving object continue to move at a constant speed and in the same direction. Unless some outside force changes the object's motion. A moving item can only be made to slow down, speed up, stop, or turn by such a force. One force that commonly slows or stops a moving object is friction with other objects. The force required to change an object's motion depends on the mass of the object. The quantity of matter that makes up a thing is its mass. The greater an object's mass, the harder it is to put the object into motion or to change its direction or speed.

Inertia of Motion

Inertia of Motion describes the inability of an object to change its state of motion on its own.

Examples of Inertia of Motion

■ A fan continues to spin for a short time even after being switched off.

■ An athlete runs some distance before taking a long jump, by running the athlete gives himself larger inertia of motion.

■ A running athlete cannot stop running as soon as he reaches the finishing line.

■ A person standing on a fast-moving bus, falls forward suddenly when brakes.

Inertia of Rest

Inertia of Rest describes the inability of an object to change its state of rest on its own.

Examples of Inertia of Rest

■ As the train starts moving, a man sitting inside leans backwards because of inertia of rest.

■ The ability to drop the bottommost coin of a stack of carrom coins on a carrom board without disturbing the stack.

■ The mango falls when the mango branch is shaken suddenly.

■ The passengers in the bus lean backwards when a stopped bus suddenly moves forward.

Torque

The amount of twisting effort applied to an object by a force or forces is known as torque. Multiplying the force by the distance between the axis and the line of force yields the torque around any axis. The torque increases as the force moves farther from the axis. For this reason, a wheel turns more easily when the force is applied farther from the centre. Torque (Moment of Force) is a vector quantity.

Symbol of torque : Ļ„

Ļ„ = rF sinĪø

r = Position vector

F = Force

Īø = Angle measurement

Impulse

Impulsive Force is the application of a large force for a short period of time. For example, the force applied when hammering a nail. The total effect of a force on an object is called impulse. The momentum and momentum difference of a force experienced by an object are equal. This is the Impulse Momentum Principle.

Impulse Force = Force x Time

Equations of Motion

There exists some relation between velocity, acceleration, and the time intervals during which we study the motion of a body. These relations are called equations of motion.

They are : v = u + at

s = ut + ½at2

2as = v2 – u2

Where, v = final velocity, u = initial velocity, t = time interval, a = acceleration and s = displacement.

Newton’s Laws of Motion

First Law – Every body continues in its state of rest or uniform motion in a straight line unless compelled by an external unbalanced force.

Second Law – The rate of change of momentum is directly proportional to the external unbalanced force and takes place in the direction of the force.

F = ma, where F = Force, m = mass, a = acceleration

Third Law – To every action, there is an equal and an opposite reaction. Action and reaction are equal and opposite but they never cancel each other as they act on different objects.

Examples of Third Law – The flying of birds, Swimming, Rocket working (Newton’s third law and law of conservation of linear momentum), firing of gun (When a shot is fired from a gun, the gun recoils due to the reaction force applied by the shot on the gun)