what is the relation between linear velocity and angular velocity in a uniform circular motion.
Answers
Thus, for a given angular velocity, the linear velocity v of the particle is directly proportional to the distance of the particle from the centre of the circular path (i.e) for a body in a uniform circular motion, the angular velocity is the same for all points in the body but linear velocity is different for different points of the body.
hope it helps...
Answer:
Explanation:
Consider a particle moving with uniform circular motion in anticlock wise direction with centre O and radius r the particle cover an arc of length △s in time △t moving from A to B.
Hence the angular displacement is
△θ=
r
△s
Dividing both side by △t
△t
△θ
=
r
1
△t
△s
In the time interval △t be infinitesimally small (△t→0), then
△t→θ
lim
△t
△θ
=
r
1
[
△t→θ
lim
△t
△s
]
But
△t→θ
lim
△t
△θ
=ω and
△t→θ
lim
△t
△s
=V
∴ω=
r
V
V=rω
In vector form,
V
=
ω
×
r