5.2 Circular Motion

Question 1

What is angular displacement (θ) and state its unit

Answer 1

The change in angle of a body as it rotates around a circle

Radians (rads)

Question 2

How is angular displacement calculated

Answer 2

Angular displacement (radians) = distance travelled around the circle (m) / radius of the circle (m)

θ = S/r

Question 3

How do you convert degrees to radians

Answer 3

θ ° x π/180 = θ rads

180° = 2π rads

Question 4

What is frequency (f) and state its units

Answer 4

The number of oscillations per unit time

hertz (Hz)

Question 5

What is time period (T) and state its units

Answer 5

The time taken for one complete oscillation

Seconds (s)

Question 6

What is an oscillation

Answer 6

The time taken for the oscillator to pass the equilibrium from one side and back again fully from the other side

Question 7

What is the equation for angular velocity (ω)

Answer 7

Angular velocity (rad s^-1) = 2π / time period (s)

ω = 2π/T

Angular velocity (rad s^-1) = 2π x frequency (Hz)

ω = 2πf

Angular velocity (rad s^-1) = change in angular displacement (rad) / time (s)

ω = Δθ/Δt

Question 8

What is angular velocity (ω) and state its units

Answer 8

The rate of change in angular displacement with respect to time

Radians per second (rad s^-1)

Question 9

What is the equation for linear velocity (v)

Answer 9

Linear velocity (ms^-1) = angular velocity (rad s^-1) x radius (m)

v = ωr

Question 10

What is centripetal force (F) and state its unit

Answer 10

Te resultant force towards the centre of the circle required to keep a body in uniform circular motion. It acts perpendicular to linear velocity

Newtons (N)

Question 11

What is the equation for centripetal force (F)

Answer 11

Centripetal force (N) = mass (kg) x linear velocity² (ms^-1) / radius (m)

Centripetal force (N) = mass (kg) x angular velocity² (rad s^-1) x radius (m)

Centripetal force (N) = mass (kg) x linear velocity (ms^-1) x angular velocity (rad s^-1)

F = mv² / r = mω²r = mvω

Question 12

What is linear velocity (v) and state its unit

Answer 12

The velocity of an object rotating in uniform circular motion with respect to a linear displacement

Metres per second (ms^-1)

Question 13

What is centripetal acceleration (a) and state its unit

Answer 13

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

Metres per second² (ms^-2)

Question 14

What is the equation for centripetal acceleration (a)

Answer 14

Centripetal acceleration (ms^-2) = linear velocity² (ms^-1) / radius (m)

Centripetal acceleration (ms^-2) = angular velocity² (rad s^-1) x radius (m)

a = v²/r = ω²r