Circular motion Physics A Level

Circular Motion

What is exactly meant by circular motion ? It is the physical motion of an object moving in a circular path about a center. There are circular motion in many areas of our life, for example the hour and minute hand of a clock displays circular motion, and also the planets and moons in the solar system show circular motion.(Although planets move in elliptical paths we consider them to be moving in circular paths for calculation purposes.)

First lets look at some important maths that are a essential for understanding todays topic of circular motion.

180 degrees = π radians 360 degrees = 2π radians 90 degrees   = ½ π radians For very small angles :     sin θ  = θ radians                                                        tan θ=  θ radians

* Ѡ (the angular velocity) is the angle in radians through which the the object in circular motion has turned in one second.

*ἀ (the angular acceleration) is the increase in the value of Ѡ (the angular velocity) per second.

* r –denotes the radius of the circle that we are dealing with.

The types of circular motion:

1.      Horizontal circular motion

2.      Vertical circular motion

3.      Conic pendulum

Different situation or means of circular motion:

1.      Revolving at a constant speed around a circle.(eg: hands of a clock)

2.      Revolving with variable speeds (that is with constant angular acceleration or constant angular deceleration)

*(eg : A car starts from rest and its wheels show constant angular acceleration)

1.   Constant speed circular motion:

A particle P revolves at a constant speed in a circular path. At time ( t=0), P is at P₁. After a time t , P is there as shown in the diagram. Consider the radius of the circular path to be r.

S=r θ  (θ in radians)

Velocity

 V=s/t

V=r θ/t  (from equation 1)

θ/t= Ѡ (angular speed)

Ѡ= θ/t

(linear velocity)  V= r Ѡ ( angular velocity)

Definition of angular speed:

The rate of change in angle is the angular speed.

The unit of angular speed is rad/s.

The Dimension of angular speed is T^-1

Angular speed is a scalar quantity because it has only a magnitude.

Angular velocity id a vector quantity ,because it has both direction and magnitude.

Rotation with a constant speed:

If a body is rotating with a constant speed then tangential acceleration is equal to zero.But still there an acceleration on the body toward the center. THIS IS CALLED CENTRIPETAL  ACCELERATION!