Circular Motion
Physics
, Circular Motion
Circular Motion
θ is the angular displacement (measured in radian)
Unit of θ : rad
Angular Velocity, w
It is the rate of change of angular displacement swept by the radius.
Δθ
w=
Δt
θ
w= ⇒θ=wt
t
S.I Unit of w: rad s−1
Time Period
Time to complete 1 cycle
θ
w=
t
For 1 cycle: θ=2 π , t=T
2π
w=
T
1
Frequency of Rotation: f =
T
2π
w=
T
w=2 π ()
1
T
w=2 π f
w: Angular frequency
f: Frequency
2
, Circular Motion
Linear Speed, v
distance
speed=
time
Distance for 1 cycle = 2 π r
2π r Time for 1 cycle = T
v=
T
2π
v= ⋅r
T
r: Radius of circle
v=wr
The Radian (1 rad)
It is the angle subtended at the centre of a circle by an arc length equal to the radius.
s=r
s=r θ
θ=1rad
Centripetal Force, Fc
It is the resultant force acting towards the centre of the circular path.
3
, Circular Motion
The body is moving with uniform speed but its velocity is continuously changing since direction
of motion is changing.
This change in velocity causes the body to accelerate and the centripetal acceleration is directed
radially inwards, towards the centre. From F = ma, a resultant force is produced.
Note:
1. The velocity is always tangential to the circular path.
2. The centripetal acceleration and centripetal force have no component in the direction of
motion. Hence, the direction of velocity is always perpendicular to both centripetal acceleration
and centripetal force.
W . Dby resultant force=F × Δ r
Δ r : displacement ∈direction of force
r :const
Δ r=0
W . Dby resultant force=0 ( centripetal force )
Δ E k =0
Ek const (Speed const)
No work is done by the centripetal force because displacement in the direction of the force is
zero. Hence speed remains unchanged.
Centripetal Acceleration
a c =vw
a=( wr ) w
2
a=w r
a=v ()
v
r
, w=
v
r
4
Physics
, Circular Motion
Circular Motion
θ is the angular displacement (measured in radian)
Unit of θ : rad
Angular Velocity, w
It is the rate of change of angular displacement swept by the radius.
Δθ
w=
Δt
θ
w= ⇒θ=wt
t
S.I Unit of w: rad s−1
Time Period
Time to complete 1 cycle
θ
w=
t
For 1 cycle: θ=2 π , t=T
2π
w=
T
1
Frequency of Rotation: f =
T
2π
w=
T
w=2 π ()
1
T
w=2 π f
w: Angular frequency
f: Frequency
2
, Circular Motion
Linear Speed, v
distance
speed=
time
Distance for 1 cycle = 2 π r
2π r Time for 1 cycle = T
v=
T
2π
v= ⋅r
T
r: Radius of circle
v=wr
The Radian (1 rad)
It is the angle subtended at the centre of a circle by an arc length equal to the radius.
s=r
s=r θ
θ=1rad
Centripetal Force, Fc
It is the resultant force acting towards the centre of the circular path.
3
, Circular Motion
The body is moving with uniform speed but its velocity is continuously changing since direction
of motion is changing.
This change in velocity causes the body to accelerate and the centripetal acceleration is directed
radially inwards, towards the centre. From F = ma, a resultant force is produced.
Note:
1. The velocity is always tangential to the circular path.
2. The centripetal acceleration and centripetal force have no component in the direction of
motion. Hence, the direction of velocity is always perpendicular to both centripetal acceleration
and centripetal force.
W . Dby resultant force=F × Δ r
Δ r : displacement ∈direction of force
r :const
Δ r=0
W . Dby resultant force=0 ( centripetal force )
Δ E k =0
Ek const (Speed const)
No work is done by the centripetal force because displacement in the direction of the force is
zero. Hence speed remains unchanged.
Centripetal Acceleration
a c =vw
a=( wr ) w
2
a=w r
a=v ()
v
r
, w=
v
r
4
