Unit 3.1 Circular Motion

Question 1

Define radian
(2-way)

Answer 1

• An angle such that
• the arc length = radius of the circle

Question 2

Why does the radian have no unit?

Answer 2

It’s a ratio of two lengths

Question 3

Hence, the equation for finding the radian in a sector of a circle?
(Not in data booklet)

Answer 3

θ = c/r

Question 4

Define θ?
(Finding radian in a circle)

Answer 4

Radian…
(No unit/rad)

Question 5

Define c?
(Find radian in a circle)

Answer 5

Circumference
or
Arc length
(m)

Question 6

Define r?
(Find radian in a circle)

Answer 6

Radius
(m)

Question 7

How to convert between radians and degrees
(Basic principles)
(3-way)

Answer 7

• 360° in one revolution of a circle
• corresponding to 2π radians

2π = 360°

Question 8

Degree to radians?

Answer 8

Deg x π/180

Question 9

Radians to degree?

Answer 9

Rad x 180/π

Question 10

But then, what’s the equation for finding the arc length?
(Noot in data booklet)

Answer 10

Arc length c = rθ

Question 11

Define angular velocity ω
(3-way)

Answer 11

• Suppose an object moves with
• constant motion through an angle θ
• in a time t

Question 12

Therefore, angular velocity equation?
(In data booklet)

Answer 12

ω = θ/t

Question 13

Define ω?
(Angular velocity eqn)

Answer 13

Angular velocity
(rads^-1)

Question 14

Define θ
(Angular velocity eqn)

Answer 14

Angle in radians
(rad)

Question 15

Define t
(Angular velocity eqn)

Answer 15

Time in seconds
(s)

Question 16

What about angular velocity for one complete revolution?
(NOT IN DATA BOOKLET)

Answer 16

ω = 2π/T

Question 17

Define T?
(P_oint.E_vidence)

Answer 17

• Period
• Time taken for one revolution

Question 18

Define F?
(P_oint.E_vidence)

Answer 18

• N° of revolutions
• per unit time

Question 19

Hence, equation for number of revolutions?
(NOT IN DATA BOOKLET)

Answer 19

F = 1/T

Question 20

What can ω also be defined as?

Answer 20

Angular frequency

Question 21

Equation for angular frequency?
(NOT IN DATA BOOKLET, ofc)

Answer 21

ω = 2πf

Question 22

How can angular frequency be derived from?
(3 by 3 steps)

Answer 22

• ω = 2π/T (aka “for 1 complete revolution”)
• ω = 2π/(1/F)
• ω = 2πf

Question 23

Equation for the instantaneous linear velocity V?
(in data booklet)

Answer 23

V = ωr

Question 24

Define V
(Instantaneous linear velocity eqn)

Answer 24

… instantaneous velocity
(ms^-1)

Question 25

Define ω (Instantaneous linear velocity eqn)

Answer 25

Angular velocity (rads^-1)

Question 26

Define r (Instantaneous linear velocity eqn)

Answer 26

Radius (m)

Question 27

Show that V = ωr? (Whiteboard) (5-way)

Answer 27

- The diagram, then: - V = d/t - = c/t - = rθ/t - HENCE, V = ωr

Question 28

Define centripetal acceleration a? (4-way)

Answer 28

- When an object moves with constant motion, - in a circle it must be - accelerating even though - ω is constant

Question 29

3 jigs with centripetal acceleration?

Answer 29

- **Acceleration is towards centre of circle** - Speed is constant - Direction of velocity is always changing

Question 30

HENCE, eqn for centripetal acceleration? (In data booklet)

Answer 30

a = V²/r

Question 31

Define a? (Centripetal acceleration eqn)

Answer 31

... centripetal acceleration (ms^-2)

Question 32

Define V²? (Centripetal acceleration eqn)

Answer 32

Instantaneous velocity **squared** (ms^-1)

Question 33

Define r? (Centripetal acceleration eqn)

Answer 33

Radius of circle (m)

Question 34

Show how centripetal acceleration can also be written as: a = ω²r (In data booklet actually) (4-way) (Whiteboard)

Answer 34

- a = V²/r - = (ωr)²/r - = ω²r - Hence: a = ω²r

Question 35

What is meant by "centripetal force"? (2-way)

Answer 35

- A force which acts on a body moving - in a circular path

Question 36

Which direction does the centripetal force act? Draw it too…. (Whiteboard) (2-way)

Answer 36

- Directed towards - the centre of the circle

Question 37

Centripetal force eqn w/ v? (In data booklet)

Answer 37

F = mv²/r

Question 38

Centripetal force eqn w/ ω? (In data booklet)

Answer 38

F = mω²r

Question 39

What's the difference between 2 of the centripetal force eqn's? (Both in data booklet)

Answer 39

- One involves **instantaneous velocity** - Other involves **angular velocity**

Question 40

Do u know some examples of centripetal force? (THE, booklet)

Answer 40

Page 6... onwards

Question 41

This topic is heavily based on ppq....

Answer 41

... cuz it's heavily based on problem solving