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
1 radian = (3600/2p) =57.30
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 )
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