16 - Circular Motion

Question 1

Define the radian.

Answer 1

The angle subtended by a circular arc with a length equal to the radius of the circle.

Question 2

What is 360° in radians?

Answer 2

360° = 2π radians

Question 3

How do you convert between radians and degrees?

Answer 3

Divide the angle by π.

Question 4

What is angular velocity of an object in circular motion?

Answer 4

The rate of change of angle.

Question 5

What is the frequency of an object in circular motion?

Answer 5

The number of rotations per unit time. (Hz)

Question 6

What is the frequency of an object in circular motion?

Answer 6

The time taken to complete one rotation. (Seconds)

Question 7

What are the two equations for angular frequency?

Answer 7

ω = 2πf

ω = 2π / T

Question 8

What is the symbol for angular frequency

Answer 8

ω

Question 9

What is the most commonly used unit for angular frequency?

Answer 9

rad s⁻¹

Radians per second

Question 10

What does any object require in order to accelerate?

Answer 10

A resultant force to be acting on it.

Question 11

What is centripetal force?

Answer 11

Any force that keeps a body moving with a uniform speed along a circular path.

Question 12

In what direction does a centripetal force always act?

Answer 12

Perpendicular to the velocity of the object.

Towards the centre of the circle.

Question 13

What would the centripetal force be in the following situations?

• Car going round a bend
• Satellite in orbit
• Yo-yo swung on a string

Answer 13

• Friction
• Gravity
• Tension

Question 14

How do we calculate the velocity of an object in circular motion?

Answer 14

v = ωr

Speed = Distance / Time

One rotation: Distance = 2πr (Circumference)
Time = T (Period)

                   2πr / T --> ωr    (ω = 2π / T)

Question 15

What is the linear velocity at any instance proportional to?

Answer 15

v ∝ r

Question 16

What is centripetal acceleration?

Answer 16

The acceleration of any object travelling in circular motion at a constant speed.

Question 17

What direction does centripetal acceleration always act?

Answer 17

Perpendicular to velocity.

Towards the centre of the circle.

Question 18

What are the two equations for centripetal acceleration?

Answer 18

a = v² / r

a = ω²r

Question 19

What equation for force do we combine with an equation for centripetal acceleration to get centripetal force?

Answer 19

F = ma

Question 20

What are the two equations for centripetal force?

Answer 20

F = mv² / r

F = mω²r

Question 21

What happens if the centripetal force is not great enough?

Answer 21

The object does not follow circular motion and the radius of the circle will increase.

Question 22

How do banked surfaces increase the velocity that vehicles can go round corners at?

Answer 22

It means that it is not just friction but a horizontal component of the normal contact force that provides centripetal force, meaning this is greater.