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1
Office: No. 25-01, 35-01 Jalan Austin Heights 3/1, Taman Mount Austin (Tel: 07-3616538)
Branch: No. 15A, 17A, 21A & 41A Jalan Indah 16/12, Taman Bukit Indah (Tel: 07-2349168)
Name : Lecturer : Cheng Wui Leap
Subject : A Level Physics (A2) Class : A2 Physics
Chapter : 7 Motion in a Circle Lesson No : 1
Date : 14-6-2014
Topic : Kinematics of circular motion, centripetal
acceleration & force
Day/Time: Sat 11.30am –
1.30pm
A2 [18]
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1
Office: No. 25-01, 35-01 Jalan Austin Heights 3/1, Taman Mount Austin (Tel: 07-3616538) Branch: No. 15A, 17A, 21A & 41A Jalan Indah 16/12, Taman Bukit Indah (Tel: 07-2349168)
Name : Lecturer :
Cheng Wui Leap
Subject :
A Level Physics (A2)
Class :
A2 Physics
Chapter :
7 Motion in a Circle
Lesson No :
1
Date :
14-6-2014
Topic :
Kinematics of circular motion, centripetal acceleration & force
Day/Time:
Sat 11.30am
–
1.30pm A2 [18] Chapter Topic
7 Motion in a Circle 8 Gravitational Field 11 Ideal Gases 12 Temperature 13 Thermal Properties of Materials 14 Oscillations 17 (AS) Electric Fields 18 Capacitance 21 Magnetic Fields 22 Electromagnetism 23 Electromagnetic Induction 24 Alternating Currents 25 Charged Particles 26 Quantum Physics 27 (AS) Nuclear Physics
28 Direct Sensing 29 Remote Sensing 30 Communication Information Scheme of Assessment PAPER TYPE DURATION MARKS WEIGHTING AS Level A Level
1 MCQ 1 hr 40 31 % 15 % 2 Structured 1 hr 60 46 % 23 % 3 Practical 2 hr 40 23 % 12 %
4 Structured (12Qs)[8+4] 1 hr 45 min 100 38 % 5 Planning, Analysis and Evaluation (2Qs) 1 hr 15 min 30 12 %
2
sr
s;s r r r 1radr
angle(deg)angle(rad)x180
2rad360rad180
Definitions
Angular displacement (
)
–
the angle in
radian
through which a point has been rotated about centre of circle (rad).
Angular velocity (
)
–
rate of change of
angular displacement
with time (rad s
-1
)
Centripetal force
–
a force acting on a body causing it to move in a
circular
path.
Angle in radians
When dealing with circles and circular motion, it is more convenient to measure angles and angular displacements in units called
radians
rather than in degrees.
All the formulas that you are going to study later are based on
radians.
If an object moves a distance
s
around a circular path of radius
r
, its angular displacement
in radians is:
One
radian
is the angle subtended at the
centre
of a circle by an arc of length equal to the
radius
of the circle.
Conversion of angl
e between degrees and radians
If an object moves all the way around the circumference of a circle:
2r 2radr
* a complete circle contains 2
rad.
We can also say that the object has moved through 360°. Therefore:
To convert angles from degree to radian:
Whenever an angle is expressed in radian, DO NOT omit the unit
rad
!! Example: 0.75 rad or 0.5
rad
PITFALL PREVENTION
Acceleration in physics is defined as a change in the velocity,
NOT
a change in the speed (contrary to popular belief). In circular motion, the velocity vector is changing in direction, so there is indeed an acceleration.
3
22f T
sr;trrtvr tt
Angular velocity and speed
angular displacementangular velocity = = time takent
If one circle is completed, angular displacement is 2
, and time taken is T (period). so,
2f
distancesspeedvtime takent
since so,
vr
Exercise 1.
The period of a particle which moves at speed v in a horizontal circle of radius r is A
2
v
B
2
v
C
2
r v
D
2
vr
2.
The radius of the Earth is 6400 km and it takes 24 hours to make a complete rotation about its axis. (a)
What is the angular velocity of the Earth's rotation about its axis in rad s
-1
? (b) What is the speed of a person standing on the equator as the Earth rotates?
4
3.
[NOV07/4/la] (a) Explain (i) what is meant by a radian [2] (ii) why one complete revolution is equivalent to an angular displacement of 2
rad [1]
Centripetal acceleration and force
Uniform circular motion is a case where the
speed
of a rotating/circulating object is
constant
. In other word,
a
t
= 0
.
This is the case that we will study.
In a uniform circular motion, speed is constant but
velocity
is NOT due to the changing
direction
.
Centripetal acceleration is produced by a change in
direction
, not SPEED!
Example of uniform circular motion: Earth orbiting the Sun.
The gravitational pull of the Sun provides the centripetal force that keeps the Earth in its orbit.
Figure above shows a particle moving round a circle with a
steady
speed,
v
. Diagram (i) shows how the velocity vector changes from v
1
to v
2
as the particle travels anti-clockwise.
In time
t
, it will move through an angle from A to B.
Referring to Diagram (ii), if v
1
and v
2
are drawn from the same point, and third vector is drawn to complete the vector diagram, this third vector will represent the
velocity change
,
v = v
2
–
v
1
.
(You should be able to realize that angle between vectors v
1
and v
2
is the same as the angular displacement,
)

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