Angular Motion

Question 1

Why is angular displacement of a complete rotation = 2pi

Answer 1

Ø= s/r
Ø = angle of sector
s = circumference of arc
r = radius of circle
For circumference s = 2pir
So Ø=2pir/r
So r cancels out so Ø=2pi

Question 2

Angular velocity

Answer 2

w
Measure of radians per second so unit is rads^-1

Question 3

Equation for instantaneous angular velocity

Answer 3

w = dØ/dt

Question 4

Periodic time

Answer 4

T, the time taken for one full rotation (s)
So revolution per second = 1/T.
Inverse of periodic time.

Question 5

Relationship between periodic time and angular velocity-

Answer 5

w=2pi/T

Question 6

Kinematic relationships for angular motion

Answer 6

Same as for for linear but
v for linear is w for angular
u for for linear is wo (small o)
t is constant
a for linear is @ for angular
s for linear is Ø (radians) for angular

Question 7

Relationship between v and r

Answer 7

v=rw

Question 8

How to derive v=rw

Answer 8

Ø=s/r differentiate both with respect to t
dØ/dt= d/dt * (s/r)
w= ds/dt 1/r
w = v1/r
v=rw

Question 9

What will the v in v=rw be representative of ?

Answer 9

It will be the tangential velocity of the object moving in a circle and will be perpendicular to the radius at any point