1. Advanced Higher Physics Unit 1
Angular motion

2. Angular motion Many motions follow a curved path.
θ angular displacement ,measured in radians (rad)
w angular velocity, measured in radians per second (radsˉ¹)
α angular acceleration, measured in radians per second per second (radsˉ²)
v rotational (tangential) velocity
a rotational (tangential) acceleration θ w v

3. Angular displacement

4. Angular velocity
Angular velocity w is defined as the change in angular displacement dθ
over time dt. dθ w

5. Example-2007 Q2(a)(ii)(A) A turntable accelerates uniformly
from rest until it rotates at 45
revolutions per minute. The time
taken for the acceleration is 1.5 s.
Show that the angular velocity
after 1.5 s is 4.7 rad.sˉ¹.
Axis of rotation
Solution

6. (This formula can be found in the data booklet)
Angular acceleration
Angular acceleration α is defined as the change in angular velocity dw
over time dt.
As with linear motion:
(This formula can be found in the data booklet)

7. Equations of angular motion
The equation of angular motion are similar to those of linear motion.
Angular motion
Linear motion
You do not need to derive these !
w◦ initial angular velocity, measured in radsˉ¹.

8. Example-2007 Q2(a)(ii)(B) A turntable accelerates uniformly
from rest until it rotates at 45
revolutions per minute. The time
taken for the acceleration is 1.5 s.
Calculate the angular acceleration of
the turntable.
Axis of rotation
Solution

9. Uniform Circular Motion
For this motion, both w and v are constant.
T is the period of the motion, that is the time for one complete
rotation.
Linear motion
Angular motion v s θ v
You need to be able to derive this!
(In data booklet)

10. Also:
(These formulas can be found in the data booklet)

11. Radial acceleration
A particle moves from A to B in time Δt with a constant speed.
Its velocity is changing (size stays the same, but direction changes).
The change in velocity Δv=v-u is: v B θ θ u -u v A θ Δv

12. v B θ s θ r u A
but so

13. As θ → 0, then a → instantaneous accelerationor
since
(can be found in the data booklet)
You need to be able to derive these!

14. Centripetal Force
This acceleration is towards the centre of the circle.
Any circular motion must have a radially inwards force responsible
for the motion (F=ma).
This force is called the CENTRIPETAL FORCE.
(In data booklet)

15. Examples: ORBIT F The centripetal force is supplied by the
gravitational force.

16. Car on a track
The centripetal force is supplied by Friction.

17. Car at the top of a bump eg: bridge
The centripetal force is supplied by weight.

18. Mass on a string-vertical circle
The centripetal force is supplied by
a combination of tension and weight.

19. Conical pendulum The centripetal force F is supplied by
component of tension T. θ T F W

20. Example-2006 Q1(a)(ii)(iv)(v)
A child’s toy consist of a model aircraft
attached to a light cord. The aircraft is
swung in a vertical circle at constant speed
as shown.
X is the highest point and Y is the lowest
point in the circle.
Time for 20 revolutions: 10.00s
Radius of circle: m
Mass of aircraft: kg Y
Calculate the centripetal force acting on the aircraft.
Draw labelled diagrams to show the forces acting on the aircraft at X and at Y.
Calculate the minimum tension in the cord.

21. Solutions 1.

22. Solutions 2.
At X
weight
tension
tension
At Y
weight

23. Solutions 3.
The minimum tension happen at X
At X