Angular Velocity

Question 1

Define angular velocity

Answer 1

Angular displacement, Δθ, is the angle through which a point is rotated

Question 2

Calculate the angle subtended by an arc of length 12 m with a radius of 4 m

Answer 2

3 rad

Question 3

Calculate the angular displacement of the edge of a door that travels 1.2 m around a bend with a radius (width) of 80 cm

Answer 3

1.5 rad

Question 4

Calculate the angular displacement of a car that travels 38 m around a bend with a radius of curvature of 15 m

Answer 4

2.5 rad

Question 5

State the angular displacement of a clock’s hour hand between 11am and 3pm

Answer 5

2.1 rad

Question 6

State the angular displacement of a passenger on a ferris wheel that does three circuits

Answer 6

6π rad

Question 7

A toy train moves round a circular track of radius 0.50 m.

a) How many radians has the train turned through in moving 1.4 m along the track?
b) What is this angle in degrees?

Answer 7

2.8 rad

180 degrees

Question 8

What is the symbol for angular velocity

Answer 8

ω = angular velocity (the rate of change of angle)

Question 9

Calculate the angular velocity of the london eye which rotates every 30mins

Answer 9

Angular displacement: 2π (one full rotation)
Time: 1800 s
Angular velocity, ω = angular displacement ÷ time
= 2π ÷ 1800
= 0.0035 rad s^-1

Question 10

What is the unit for angular velocity

Answer 10

Since angular displacement has no units, the units for angular velocity are just s^-1

Question 11

Calculate the angular velocity of a CD that rotates at 200 rpm

Answer 11

Angular displacement: 400π (200 full rotations)
Time: 60 s
Angular velocity, ω = angular displacement ÷ time
= 400π ÷ 60
= 21 rad s^-1

Question 12

Calculate the angular velocity of:
An 8 in diameter tire which rotates 8 times a second
A 10 cm fan blade which rotates 85 times per second
A 12 cm CD which rotates 12 600 times a minute
A minute hand on a clock
A spinning top which travels π radians in a third of a second
A ferris wheel which takes 11 minutes to do one revolution
A microwave turning plate which travels half a revolution in 20 seconds

Answer 12

50 rad s^-1
530 rad s^-1 
1320 rad s^-1 
1.75 x 10^-3 rad s^-1 
9.4 rad s^-1 
9.5 x 10^-3 rad s^-1 
0.16 rad s^-1

Question 13

What is Time period?

Answer 13

The time for one full revolution

Question 14

Calculate the linear velocity of a child sitting 0.60 m from the centre of a playground roundabout which has an angular velocity of 1.4 rad s-1

Answer 14

Angular velocity: 1.4 rad s-1
Radius: 0.6 m
linear velocity, v	= angular velocity x radius
				= 1.4 x 0.6
				= 0.84 m s^-1

Question 15

A person standing on the equator will be moving due to the rotation of the Earth (r = 6400 km).
What is their angular velocity?
What is their instantaneous linear velocity?

Answer 15

a. Angular displacement: 2π (1 full rotation)
Time: 86400 s (24 h)
Angular velocity, ω = 2π ÷ 86400 = 0.00007272205 = 7.3 x 10-5 rad s^-1

b. Angular velocity: 0.00007272205 rad s^-1
Radius: 6 400 000 m
linear velocity, v = 0.00007272205 x 6400000 = 470 m s^-1

Question 16

The minute hand on a watch is 6.4mm long. Calculate its frequency, its angular speed and the speed of its free end

Answer 16

a) 2.78 x 10^-4
b) 1.75 x 10^-3
c) 1.12 x 10^-5

Question 17

The information on a CD is recorded as a series of bumps in the tracks on the CD. The information is ‘read’ by a laser beam. Calculate the speed of the bumps moving past the laser head at 4.0cm from the centre of a CD which is rotating at 430 rpm

Answer 17

a. Angular displacement: 860π (430 full rotation)
Time: 60 s (per minute)
Angular velocity, ω = 860π ÷ 60 = 45.02949 = 45 rad s-1

b. Angular velocity: 45.02949 rad s-1
Radius: 0.04 m (4.0 cm)

linear velocity, v = 45.02949 x 0.04 = 1.8 m s-1