Unit 4: Motion in a circle

Question 1

What is uniform circular motion?

Answer 1

When an object rotates at a steady rate

Question 2

What is the formula for frequency?

Answer 2

f = 1/T where T is the time for one rotation

Question 3

What is the formula for velocity and how is it derived?

Answer 3

v = 2πr/T and it is derived through distance travelled which is the circumference/time taken for one rotation

Question 4

How do you calculate the number of rotations in one minute?

Answer 4

Multiply the frequency of rotation by 60

Question 5

What does an object in uniform circular motion turn through an angle of each second?

Answer 5

2π/T radians where T is the time for one complete rotation

Question 6

What are the formulas for the angular displacement of an object in time t?

Answer 6

2πt/T or 2πft

Question 7

What is angular speed defined as?

Answer 7

The angular displacement per second

Question 8

What is the formula for angular speed?

Answer 8

ω = 2πf

Question 9

What is ω measured in?

Answer 9

Radians per second

Question 10

What is the formula for velocity in terms of ω?

Answer 10

v = rω

Question 11

What is the formula for the length of an arc?

Answer 11

s = rθ

Question 12

Why does an object accelerate when it is travelling in a circle?

Answer 12

The velocity of an object moving around a circle at constant speed continuously changes direction

Question 13

What is acceleration?

Answer 13

The change of velocity per second

Question 14

In which direction is the velocity of an object at any point in a circle?

Answer 14

Along the tangent to the circle at that point

Question 15

Why is the acceleration towards the centre of the circle and what is this acceleration called?

Answer 15

The change in direction of the velocity is towards the centre of the circle therefore the acceleration is towards the centre of the circle and this type of acceleration is centripetal acceleration

Question 16

What is the formula for centripetal acceleration in terms of v?

Answer 16

a = v^2/r

Question 17

What is the formula for centripetal acceleration in terms of ω?

Answer 17

a = rω^2

Question 18

What type of quantities are acceleration and velocity?

Answer 18

Vectors

Question 19

In which direction does the acceleration of an object act?

Answer 19

In the same direction as the resultant force

Question 20

What is the centripetal force referred to as and in which direction does it act?

Answer 20

The resultant force on an object moving round a circle at constant speed and it acts towards the centre of the circle

Question 21

What are the formulas of the centripetal force?

Answer 21

F = mrω^2 or F = mv^2/r

Question 22

How is the formula for centripetal force derived?

Answer 22

Through using Newton’s second law i.e. F = ma

Question 23

What is required to make an object move round on a circular path?

Answer 23

It must be acted on by a resultant force which changes its direction of motion

Question 24

Why is no work done by the centripetal force and what is the effect on kinetic energy?

Answer 24

This force is at right angles to the direction of the object’s velocity and there is no displacement in the direction of the force therefore the kinetic energy of the object is constant and so the speed is unchanged

Question 25

What is the centripetal force for an object whirling around on the end of a string?

Answer 25

The tension in the string

Question 26

What is the centripetal force for a satellite moving round the Earth?

Answer 26

The force of gravity between the satellite and the Earth

Question 27

What is the centripetal force for a planet moving around the sun?

Answer 27

The force of gravity between the planet and the sun

Question 28

What is the centripetal force for a capsule on the London Eye?

Answer 28

The centripetal force is the resultant of the support force on the capsule and the force of gravity on it

Question 29

When using a magnetic field to bend a beam of charged particles, what is the centripetal force?

Answer 29

The magnetic force on the moving charged particles

Question 30

What is required to make an object move on a circular path?

Answer 30

The object must be acted on by a resultant force which is always towards the centre of the curvature of its path

Question 31

Why is a road banked?

Answer 31

To enable vehicles to drive round without any sideways friction on the tyres and on a banked track, the speed can be higher

Question 32

What is the centripetal force on a road vehicle provided by without any banking?

Answer 32

Sideways friction between the vehicle wheels and the road surface

Question 33

What can happen to a vehicle on a bend if the speed is too high?

Answer 33

The vehicle can slip outwards

Question 34

What centripetal acceleration values can be dangerous to the average person?

Answer 34

Values of more than 2-3g

Question 35

What is the angle in radians defined as?

Answer 35

The arc length divided by the radius of the circle

Question 36

How many radians are there in a complete circle?

Answer 36

2π

Question 37

What is another name for linear speed v?

Answer 37

Tangential velocity

Question 38

What is the frequency of an object in circular motion?

Answer 38

The number of complete revolutions per second

Question 39

What is frequency measured in?

Answer 39

Hz

Question 40

What would happen if the centripetal force of an object travelling in a circle were removed?

Answer 40

The object would fly off at a tangent

Question 41

Why do the particles in a cyclotron (a type of particle accelerator) have the same angular speed yet different linear speeds?

Answer 41

They have different linear speeds as their distances from the centre varies however they have the same angular speed as they all rotate through the same angle in the same time