Relate linear velocity and angular velocity.
Answers
Answer:
The linear velocity of the particle is related to the angular velocity. While considering the rotational motion of a rigid body on a fixed axis, the extended body is considered as a system of particles moving in a circle lying on a plane that is perpendicular to the axis, such as the centre of rotation lies on the axis.
Explanation:
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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