Circular Motion

Question 1

What is the term given to an object rotating at a steady rate?

Answer 1

Uniform circular motion

Question 2

If an ball on a string is travelling in a circle in the vertical plane, where are the points of minimum and maximum tension?

Answer 2

Minimum tension at the top

Maximum tension at the bottom

Question 3

Define centripetal force

Answer 3

The resultant force that makes the object move in a circle

Question 4

Why do planes turn when at an angle?

Answer 4

The lift force is comprised of a horizontal and vertical component.

The horizontal component provides the centripetal force causing it to turn.

Question 5

How do you convert degrees -> radians

Answer 5

Question 6

How do you convert radians -> degrees

Answer 6

Question 7

Define angular displacement

Answer 7

The angle through which an object in circular motion travels in a given time

Question 8

How do you deal with rpm? (revolutions per minute)

Answer 8

÷60 to convert to rps (revolutions per second)

Then set rps = frequency

Question 9

Define frequency

Answer 9

The number of complete oscillations per second

Question 10

What is the equation for linear velocity?

Answer 10

Question 11

Why is an object in circular motion accelerating?

Answer 11

Its linear velocity does not change in magnitude

But is constantly changing in direction

Question 12

In circular motion which direction do the acceleration and centripetal force vectors act?

Answer 12

Always towards the centre

Question 13

What is the condition for circular motion to happen?

Answer 13

A velocity needs to be acting perpendicular to a resultant force

Question 14

What happens if…

F_centri > F_max

Answer 14

Circular motion does not happen

(Eg car skids off the road or moves to a higher radius)

Question 15

What happens if…

F_{centri ≤} F_max

Answer 15

Circular motion happens

(eg friction is large enough to keep car on track)

Question 16

What is F_centri for an object at the top of the vertical circle?

Answer 16

Question 17

What is F_centri for an object on top of a vertical circle?

Answer 17

Question 18

What is F_centri for an object at the bottom of a vertical circle?

Answer 18

Question 19

How do you find out the minimum velocity for an object travelling in a vertical circle?

Answer 19

Set R=0 (or tension if ball on string)

And rearrange for v

Question 20

How do you find out the maximum velocity for an object travelling over a vertical circle? (eg car over a hill)

Answer 20

Set reaction R=0

Then rearrange for v

Question 21

When solving angled circular motion problems what are the 3 usual steps?

Answer 21

1. Set vertical component tension = weight
2. Work out horizontal component of tension using trig
3. F_centri = horizontal component

Question 22

Why can’t a ball be swung around in a circle with the string horizontal?

Answer 22

There must be a vertical component of the tension to match the weight

Otherwise ball is not in vertical equilibrium

Question 23

What is the equation for angular velocity? (there are 3 equations)

What are the units?

Answer 23

(change in θ)/(change in time)

2π /T or 2π f

Units of rad.s^-1

Question 24

What is the formula for the length of an arc?

Answer 24

s = rθ

s - arc length (m)

r - radius (m)

Question 25

What happens to a ball in conical circular motion as it speeds up?

Answer 25

• centripetal force must increase
• Therefore, horizontal component of tension increases
• This means resultant tension acts at a flatter trajectory
• String will rotate in a more horizontal path
• This means θ between the vertical centre and the string will increase but will never reach 90 degrees as the weight of the ball prevents this