Module 5: Chapter 16 - Circular Motion

Question 1

What is the equation for the linear speed of an object in uniform circular motion?

Answer 1

v = 2πr/T

v = 2πrf

r = radius, T = period, f = frequency

Question 2

What is angular displacement (θ)?

Answer 2

The angle swept out at the centre of a circular path (in radians)

Question 3

What is the equation for arc length?

when in radians

Answer 3

s = rθ
arc length = radius x θ

Question 4

What is angular speed (ω)?

Answer 4

The rate of change of angular displacement

Question 5

What is the equation for angular speed (ω)?

Answer 5

angular speed = angular displacement / time

ω = Δθ/t
ω = 2π/T

t = time, T = period

Question 6

What are the units for angular speed?

Answer 6

rad s⁻¹

(can also be r.p.m)

Question 7

What is angular frequency?

Answer 7

Angular frequency is the same as angular speed

Question 8

What is the equation for angular frequency?

Answer 8

ω = 2πf

Question 9

Show how angular frequency is the same as angular speed:

Answer 9

Angular speed = Δθ/t
= 2π/T
= 2π 1/T
= 2πf
= Angular frequency

T = time for one full revolution

Question 10

What is the relationship between angular and linear speed?

Answer 10

v = rω

linear speed = radius x angular speed

Question 11

Derive the relationship between angular and linear speed?

Answer 11

ω = 2π/T

v = 2πr/T
= r x 2π/T
= rω

Question 12

What is centripetal acceleration?

Answer 12

The acceleration of any object travelling in a circular path at constant speed, which always acts towards the centre of the circle

Question 13

What are the 3 equations for centripetal acceleration?

Answer 13

• a = v²/r
• a = rω²
• a = vω

v = linear speed, r = radius, ω = angular speed

Question 14

What is the radius of the earth?

Answer 14

6400km

Question 15

What is the height above sea level of the iss’s orbit?

Answer 15

400km

Question 16

What are the 4 equations for centripetal force?

Answer 16

• F = mv²/r
• F = mrω²
• F = mvω
• F = ma

m =mass, v =linear speed, ω = angular speed, a = centripeal acceleration

Question 17

What is centripetal force?

Answer 17

The resultant force that keeps a body moving with a constant speed in a circular path

Question 18

A mass of 300g is whirled around a vertical circle using a piece of string of length 20cm at 3.0 revolutions per second. Calculate the tension in the string at positions:
a) Top
b) Bottom
c) String Horizontal

Answer 18

a) 18.4 N
b) 24.3 N
c) 21.3 N

Question 19

What is the expression for the centripetal force at each position?

Answer 19

a) CF = T + W
b) CF = T
c) CF = T - W

T = Tension, W = Weight

Question 20

What happens if centripetal force is removed?

Answer 20

The object will continue along a straight line tangentially to the circular path

Question 21

The maximum speed of a car (without skidding) of mass 750kg around a roundabout of radius 20m is 9ms⁻¹, calculate the centripetal force at this speed

Answer 21

3038N

Question 22

A car is racing on a track banked at 25 degrees to the horizontal on a bend with a radius of curvature of 350m. Show that the maximum speed at which the car can take the bend without sideways friction is 40ms⁻¹

VERY IMPORTANT QUESTION

Answer 22

Question 23

What will happen to a car if it takes a bend at increasing speeds?

Answer 23

The radius of the cars circular motion will increase

Question 24

Explain how questions involving banked slopes can be calculated:

IMPORTANT

Answer 24

As there is a normal force acting on the object due to the banked slope, it can be resolved into vertical and horizontal components. We assume the vertical component of N balances out the weight, from this you can then calculate N. Once you have calculated N, you can calculate the horizontal component of N which is the centripetal force

The vertical component of N does NOT actually balance out the weight, however this must be used to yield the correct result from the calculations. DO NOT RESOLVE WEIGHT TO FIND N.

Question 25

Why are you pushed into your seat at the bottom of a roller coaster and “feel heavier”?

Answer 25

At the bottom of the roller coaster “Centripetal Force = Normal Force - Weight”, therefore “Normal Force = Centripetal Force + Weight”. Since Weight and Centripetal Force are constant, you experience a greater force at the bottom of the roller coaster

Question 26

Why does an object in circular motion remain at a constant speed despite a resultant force acting upon in?

Answer 26

The resultant force is at 90 degrees to the velocity of the object

Question 27

What does a graph of centripetal force against v² look like?

Answer 27

Positive Linear graph

Question 28

What is the relationship between linear velocity and the radius (when the angular velocity is constant)?

Answer 28

Directly proportional