Circular Motion

Question 1

Explain how we know an object in uniform circular motion must be accelerating

Answer 1

• an object in uniform circular motion has constant linear speed
• it is continuously changing direction, and since velocity is speed in a given direction, it has a constantly changing velocity
• the object must be accelerating, as acceleration is defined as the rate of change of velocity

Question 2

State the properties of centripetal acceleration

Answer 2

• acts perpendicular to the direction of the linear speed
• centripetal means it acts towards the centre of the circular path

Question 3

State and explain the direction of the centripetal force

Answer 3

• directed towards the centre of the circle
• in the same direction as the acceleration from Newton’s second law, F = ma

Question 4

Define the angular displacement (θ) of a body in circular motion

Answer 4

Angular displacement is defined as the change in angle, in radians, of a body as it rotates around a circle

Question 5

What unit is angular displacement measured in?

Answer 5

Radians

Question 6

State the equation for angular displacement (θ)

Answer 6

Δθ = distance travelled around circle/radius of the circle

Δθ = Δs/r

Question 7

Define the radian

Answer 7

The radian is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle

Question 8

What is the angle in radians for a complete circle?

Answer 8

= circumference of circle/radius
= 2πr/r
= 2π rad

Question 9

State the equation for converting from degrees to radians

Answer 9

θ° x π/180 = θ rad

Question 10

Define the angular speed (ω) of a body in circular motion

Answer 10

The angular speed is defined as the rate of change in angular displacement with respect to time

Question 11

Is angular speed a vector or a scalar, and what is it measured in?

Answer 11

• scalar quantity
• measured in rad/s

Question 12

Give four equations for angular speed (ω)

Answer 12

ω = Δθ/Δt
ω = v/r, where v is linear speed
ω = 2π/T, where T is period of a full cycle
or ω = 2πf, where f is frequency

Question 13

Define centripetal acceleration

Answer 13

The acceleration of an object towards the centre of a circle when the object is in motion (rotating) around a circle at a constant speed

Question 14

State three equations for centripetal acceleration

Answer 14

a = v²/r
We also know that ω = v/r or v = rω
So a = rω²
Or we can combine a = v²/r and r = v/ω
To give a = vω

Question 15

Define centripetal force

Answer 15

The resultant force towards the centre of the circle required to keep a body in uniform circular motion. It is always directed towards the centre of the body’s rotation.

Question 16

State three equations for centripetal force

Answer 16

F = mv²/r
F = mrω²
F = mvω

These equations all come from Newton’s second law, F = ma

Question 17

Give examples of centripetal force

Answer 17

• friction between car tyres and the road when a car travels around a roundabout
• tension in a rope when a ball on the end of the rope moves in a circle
• gravitational force on the Earth orbiting the Sun