Further Mechanics and Thermal Physics (1): Motion in a Circle

Question 1

What unit is used for angles in SHM and circular motion?

Answer 1

radians

Question 2

An object rotating at a steady speed is said to be in…?

Answer 2

Uniform circular motion

Question 3

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

Answer 3

v = 2(pi)r/T

OR

v = 2(pi)rf

where:
2(pi)r - the circumference of the circle
T - the time taken for the object to complete one full rotation
f - frequency of rotation = 1/T

Question 4

For a cyclist travelling at speed x, what is the speed of the perimeter of each wheel?

Answer 4

x ms^-1

Question 5

What is the equation for angular displacement per second?

Answer 5

2(pi)/T

where:
T - the time taken for the object to complete oen full rotation

Question 6

What is the equation for the angular displacement, theta, of an object in time t?

Answer 6

theta = 2(pi)t/T

OR

theta = 2(pi)ft

where:
theta - angular displacement
2(pi)/T - the angular displacement per second

Question 7

What is the definition of angular displacement?

Answer 7

The radians swept by an object per second

Question 8

What is the definition of angular speed, omega (lowercase)?

Answer 8

The angular displacement per second

Question 9

What is the equation for angular speed?

Answer 9

omega = theta/t = 2(pi)t/T/t = 2(pi)/T

OR

2(pi)f

Question 10

What is the unit of angular speed?

Answer 10

rads^-1

Question 11

How do you convert from x radians to degrees?

Answer 11

180/(pi) multiplied by x radians = degrees

Question 12

How do you convert from y degrees to radians?

Answer 12

(pi)/180 multiplied by y degrees = radians

Question 13

What is the equation for the linear distance, s travelled by a particle in uniform circular motion in time, t?

Answer 13

s = vt = 2(pi)rt/T = (theta)r

theta = angular displacement in time t = 2(pi)t/T

Question 14

What is the equation for the linear velocity for a particle in circular motion?

Answer 14

v = 2(pi)r/T = (omega)r

omega = angular speed = 2(pi)/T

Question 15

Describe why objects in circular motion experience a constant force?

Answer 15

• Objects moving in a circular path are constantly changing direction but moving at a constant speed
• therefore, they have a constantly changing velocity and due to Newtons 1st law an object with a changing velocity is acted upon by a resultant force

OR

• therefore, the object is accelerating and due to Newtons 2nd Law, F = ma, an object that is accelerating must be acted on by a resultant force in the direction of the acceleration

Question 16

What direction does centripetal acceleration act for an object in circular motion?

Answer 16

Towards the centre of the circle

Question 17

What direction does centripetal force act for an object in circular motion?

Answer 17

Towards the centre of the circle

Question 18

What is acceleration?

Answer 18

The change in velocity per second/ the rate of change of velocity

Question 19

What direction does the velocity act for an object in uniform circular motion?

Answer 19

Tangent to the circle

Question 20

How does the velocity of an object in uniform circular motion change as it moves around the circle?

Answer 20

The change in direction of the velocity is towards the centre of the circle

Question 21

What is the name for the type of acceleration in uniform circular motion?

Answer 21

Centripetal acceleration

Question 22

What is the equation for centripetal acceleration (linear speed)?

Answer 22

a = v^2/r

Question 23

What is the equation for centripetal acceleration (angular speed)?

Answer 23

a = (omega)^2r

Question 24

What is the name for the type of force in uniform circular motion?

Answer 24

centripetal force

Question 25

What provides the centripetal force for an object being whirled around on the end of a string?

Answer 25

Tension in the string

Question 26

What provides the centripetal force for an object in a circular orbit?

Answer 26

The force of gravity between the object and the massive planet

Question 27

What is the equation for centripetal force of an object moving with uniform circular motion? (linear speed)

Answer 27

F = mv^2/r

as F = ma

Question 28

What is the equation for centripetal force of an object moving with uniform circular motion? (angular speed)

Answer 28

F = m(omega)^2r

Question 29

What is the equation for a the centripetal force of a car travelling over the top of a curved hill?

Answer 29

mg - S = mv^2/r

where:
S - The support force from the ground onto the car
mg - The weight of the car

Question 30

What happens to the support force, S, on a car when th vehicle exceeds a certain speed and loses contact with the road over a curved hill?

Answer 30

S = 0N

Question 31

What is the maximum v^2/r can equal for a car to remain on the ground when going over a curved hill?

Answer 31

v^2/r < 9.81

Question 32

What is the centripetal force when a car is going round a roundabout?

Answer 32

The sideways force between the tyres and the road surface

Question 33

What is the maximum frictional force of a material dependant on?

Answer 33

Its coefficient of friction

Question 34

If the speed of a car moving around a roundabout is too high, what happens?

Answer 34

The car slips/skids