## 28 April 2013

### IX Motion And Rest Formative Check Points For FA-01

Circular Motion CBSE Class 9th
Q.What is circular motion.Is circular motion  an acceleration motion?
Motion of a  body  along a circle (circular path), is called a circular motion. Circular motion is an acceleration motion because velocity changes due to the change in the direction of motion.
When an object moves in a circular path with uniform speed, its motion is called uniform circular motion.
Q. Take a piece of thread and tie a small piece of stone at one of its ends. Move the stone with constant speed by holding the thread at the other end. What will be the direction in which the stone moves after it is released.
Answer: If we releas the thread , the stone moves along a straight line tangential to the circular path. This is because once the stone is released, it continues to move along the direction it has been moving at that instant.
Q. Define terms (i) One radian (ii)  Angular displacement (iii) Angular velocity
Answer: One radian is defined as the angle subtended at the centre of the circle by an arc equal in length to its radius.
Angular displacement : In a circular motion, the angular displacement of a body is the angle subtended by the body at the centre in a given interval of time. It is represented by the symbol q (theta).
Angular velocity : The angular displacement per unit time is called the angular velocity. it is represented by the symbol w(omega).
Angular velocity w = q/t
In figure, the arc AB of the circle has length l  and subtends an angle q at the centre C.
Then, q = l /r radians
[For l  = 1, q = 1 radian]
Angle subtended by the circumference at the centre, q = 2pr/r =2p radian
For complete circle at centre 2p radian = 3600
Q. Determine relation between linear velocity and Angular velocity.
Ans: Consider a body moving along the circumference of a circle of radius r with linear velocity v. Its angular velocity is ω.
Let the body moves from A to B in a time t and ө is the angle covered

Let AB = S = displacement
Linear velocity = displacement / time
v = AB/t
v= St  …………(1)
If ө is the angle subtended by an arc of length s and radius r. Then  S = r ө …………(2)
Substituting (2) in (1),
v = r ө/t
But ө/t = ω = angular velocity
v = r ω
Linear velocity = Radius of the circle x Angular velocity
Q. What do you mean by centripetal force and centrifugal force?
Answer: The constant force that acts on the body along the radius towards the centre and perpendicular to the velocity of the body is known as centripetal force.
Let us consider an object of mass m, moving along a circular path of radius r, with an angular velocity ω and linear velocity v.
F = (mv2)/r
Again, centripetal force, F = mrω2     [( since v = rω )