Short notes: Motion (theory)

Rest

When an object does not change its position with respect to a reference point with elapse of time, the object is said to be in rest.

Motion

If an object changes its position with respect to a reference point with elapse of time, the object is said to be in motion.

To observe the motion of any object; two things are necessary – a reference point and time.

Motion along a straight line

When an object moves along a straight line, the motion of the object is called rectilinear motion. For example; motion of a vehicle along a straight road.

Distance and Displacement

Distance is the length of path covered by a moving object in the given time irrespective of direction. Distance has only magnitude and no direction.

Uniform and non-uniform motion

A moving body may cover equal distances in equal intervals of time or different distances in equal intervals of time. On the basis of above assumption, the motion of a body can be classified as uniform motion and non-uniform motion.

Uniform motion: When a body covers equal distances in equal intervals of time, however, small may be time intervals, the body is said to describe a uniform motion.

Example of uniform motion –

  • An aeroplane flying at a speed of 600 km/h
  • A train running at a speed of 120 km/h
  • Light energy travelling at a speed of 3 × 108 m/s
  • A spaceship moving at a speed of 100 km/s

Non-uniform motion: When a body covers unequal distances in equal intervals of time, the body is said to be moving with a non-uniform motion.

Example of non-uniform motion –

  • An aeroplane running on a runway before taking off.
  • A freely falling stone under the action of gravity.
  • An object thrown vertically upward.
  • When the brakes are applied to a moving car.

Speed

  • Speed of a body is the distance travelled by the body per unit time. or The rate of change of motion is called speed.
  • Unit : In SI system : m/s or ms–1
  • In CGS system : cm/s or cms–1
  • Other km/h or kmh–1
  • Important note : While comparing the speed of different bodies we must convert all speeds into same units.
  • Speed is a scalar quantity, because it has the magnitude but no direction.
  • Uniform speed :- When a body covers equal distance in equal intervals of time, the body is to be moving with a uniform speed or constant speed. Ex. : A train running with a speed of 120 km/h, An aeroplane flying with a speed of 600 km/h
  • Non-uniform speed :- When a body covers unequal distances in equal intervals of time, the body is said to be moving with non-uniform speed or variable speed. Ex. : A car running on busy road, An aeroplane landing on runway.
  • Average speed :- The average speed of the body in a given time interval is defined as the total distance travelled, divided by the time interval.
  • Instantaneous speed: The speed of a body at any particular instant of time during its motion is called the instantaneous speed of the body. It is measured by speedometer in vehicles.

Velocity

  • The velocity of a body is the displacement of a body per unit time.
  • The displacement covered by a body per unit time or the speed of a body in specified direction is called the velocity.
  • Unit: In SI system : m/s or ms_1
  • In CGS system : cm/s or cms_1
  • Other km/h or kmh_1, km/min.
  • Uniform velocity When a body covers equal displacement in equal interval of time, the body is said to be moving with a uniform velocity.
  • Conditions for uniform velocity :The body must cover equal displacement in equal intervals of time. The direction of motion of the body should not change.
  • Important note : Direction of velocity represent direction of motion of body. OR Sign of velocity represent the direction of motion of body.
  • Non-uniform velocity/variable velocity : When a body covers unequal displacement in equal intervals of time, the body is said to be moving with variable velocity. When a body covers equal distance in equal intervals of time, but its direction changes, then the body is said to be moving with variable velocity.
  • Conditions for variable velocity :It should cover unequal displacement in equal intervals of time. It should cover equal distances in equal intervals of time but its direction must change.
  • Average velocity : Total displacement divided by total time is called an average velocity.   OR  The arithmetic mean of initial velocity and final velocity for a given time period, is called average velocity.

Acceleration

  • The rate of change of velocity of a moving body with time is called acceleration.
  • Change in velocity =  final velocity(v) – initial velocity(u).
  • If body moves with uniform velocity, then v = u and then acceleration is zero i.e. a = 0.
  • Unit of accelration Acceleration = , Acceleration = , Acceleration = = m/s^2
  • In SI system is m/s^2 or ms_2
  • In CGS system is cm/s2 or cms_2
  • Positive Acceleration : If the velocity of an object increases with time in the direction of the motion of the object, then the acceleratin of the body is known as positive acceleration. In this case, the object pick up the speed in a particular direction (i.e., velocity). For example, if an object starts from rest and its velocity goes on increasing with time in the direction of its motion, then the object has positive acceleration. The direction of positive acceleration is in the direction of motion of the object.
  • Negative Acceleration : If the velocity of an object decreases with time, then the acceleration of the object is known as negative acceleration. For example, if an object moving with certain velocity is brought to rest then the object is said to have negative acceleration.
  • Acceleration without changing speed : When an object moves in a circular path with constant speed, then its velocity changes due to the change in the direction of motion of the object. hence, the object is accelerated without changing its speed. In this case, the direction of acceleration is towards the centre of the circular path.
  • Positive or negative sign of acceleration always shows the direction of acceleration or direction of force but not represent direction of motion of body.
  • Acceleration which oppose the motion of a body is called retardation or negative acceleration.
  • If sign of velocity and acceleration are same it means speed of body will always increase. If both are opposite sign it means speed of body will always decrease.
  • Uniform acceleration : When a body undergoes equal changes in velocity in equal intervals of time, the body is said to be moving with a uniform acceleration Ex. : Motion of a freely falling body, Motion of a ball rolling down on an inclined plane.
  • Non-uniform acceleration or variable acceleration : When a body describes unequal change in velocity in equal intervals of time, the body is said to be moving with non-uniform acceleration. Ex.: The motion of a bus leaving or entering the bus stop, The motion of a train leaving or entering the platform.

    Uniform circular motion

  • When an object moves in a circular path at a constant speed then motion of the object is called uniform circular motion.
  • In our everyday life ,we came across many examples of circular motion for example cars going round the circular track and many more .Also earth and other planets revolve around the sun in a roughly circular orbits.
  • If the speed of motion is constant for a particle moving in a circular motion still the particles accelerates because of constantly changing direction of the velocity.
  • If an object moves in a circular path with uniform speed, its motion is called uniform circular motion
  • Here in circular motion, we use angular velocity in place of velocity we used while studying linear motion.
  • Force which is needed to make body travel in a circular path is called centripetal force.
  • We know that the circumference of a circle of radius r is given by 2πr. If the body takes seconds to go once around the circular path of radius r, the velocity v is given by   v=2πr/t
  • One thing we must keep in mind is that uniform linear motion is not accelerated but uniform circular motion is accelerated motion.
  • Examples of uniform circular motion are
    (a) Motion of artificial satellites around the earth
    (b) Moon, the natural satellite of earth, moves in uniform circular motion round the earth.
    (c) Cyclist moving on a circular track with a constant speed exhibits uniform circular motion.
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