1. Circular Motion

2. Circular MotionAngular Velocity

3. Circular MotionAngular Velocity
O
r
Let O be the centre of a circle, radius r units.

4. Circular MotionAngular Velocity
,
where,in timetofrommovespointtheIf
AOP
tPA
O
r
Let O be the centre of a circle, radius r units.
A
P


5. Circular MotionAngular Velocity
,
where,in timetofrommovespointtheIf
AOP
tPA

 condradians/seinmeasured
time.respect to
withofchangeofratetheasdefinedispoint
theof,locity,angular ven thethe


O
r
Let O be the centre of a circle, radius r units.
A
P

6. Circular MotionAngular Velocity
,
where,in timetofrommovespointtheIf
AOP
tPA

 condradians/seinmeasured
time.respect to
withofchangeofratetheasdefinedispoint
theof,locity,angular ven thethe







dt
d
O
r
Let O be the centre of a circle, radius r units.
A
P

7. Circular MotionAngular Velocity
,
where,in timetofrommovespointtheIf
AOP
tPA

 condradians/seinmeasured
time.respect to
withofchangeofratetheasdefinedispoint
theof,locity,angular ven thethe







dt
d
Linear Velocity (Tangential Velocity)
O
r
Let O be the centre of a circle, radius r units.
A
P

8. Circular MotionAngular Velocity
,
where,in timetofrommovespointtheIf
AOP
tPA

 condradians/seinmeasured
time.respect to
withofchangeofratetheasdefinedispoint
theof,locity,angular ven thethe







dt
d
Linear Velocity (Tangential Velocity)
O
r
Let O be the centre of a circle, radius r units.
A
P
The linear velocity, v, of the point at every position on its path is
tangential to the circle.

9. Circular MotionAngular Velocity
,
where,in timetofrommovespointtheIf
AOP
tPA

 condradians/seinmeasured
time.respect to
withofchangeofratetheasdefinedispoint
theof,locity,angular ven thethe







dt
d
Linear Velocity (Tangential Velocity)
O
r
Let O be the centre of a circle, radius r units.
A
P
The linear velocity, v, of the point at every position on its path is
tangential to the circle.
v

10. Circular MotionAngular Velocity
,
where,in timetofrommovespointtheIf
AOP
tPA

 condradians/seinmeasured
time.respect to
withofchangeofratetheasdefinedispoint
theof,locity,angular ven thethe







dt
d
Linear Velocity (Tangential Velocity)
O
r
Let O be the centre of a circle, radius r units.
A
P
The linear velocity, v, of the point at every position on its path is
tangential to the circle.
Let arc AP = x
v

11. rx 

12. rx 


r
dt
d
r
dt
dx



13. rx 


r
dt
d
r
dt
dx




rv
OR
rv



14. rx 


r
dt
d
r
dt
dx




rv
OR
rv


Period

15. rx 


r
dt
d
r
dt
dx




rv
OR
rv


Period

2
T (time taken for one revolution)

16. rx 


r
dt
d
r
dt
dx




rv
OR
rv


Period

2
T (time taken for one revolution)
e.g. A satellite moves in a circular orbit of 20 rev/day
rad/sinDescribea) 

17. rx 


r
dt
d
r
dt
dx




rv
OR
rv


Period

2
T (time taken for one revolution)
e.g. A satellite moves in a circular orbit of 20 rev/day
rad/sinDescribea) 
rad/day220  

18. rx 


r
dt
d
r
dt
dx




rv
OR
rv


Period

2
T (time taken for one revolution)
e.g. A satellite moves in a circular orbit of 20 rev/day
rad/sinDescribea) 
rad/day220  
rad/s
2160
rad/s
606024
220







19. km/hin
9000km,isradiusitsgiven thatvelocity,ltangentiassatellite'theFindb)

20. km/hin
9000km,isradiusitsgiven thatvelocity,ltangentiassatellite'theFindb)
km/s
2160
9000



 rv

21. km/hin
9000km,isradiusitsgiven thatvelocity,ltangentiassatellite'theFindb)
km/s
2160
9000



 rv
km/h15000
60km/h60
2160
9000





22. km/hin
9000km,isradiusitsgiven thatvelocity,ltangentiassatellite'theFindb)
km/s
2160
9000



 rv
km/h15000
60km/h60
2160
9000




Exercise 9A; odd