Angular Displacement

Question 1

What does a radian describe?

Answer 1

A radian describes an angle using the ratio of the arc length (s) to the radius (r)

Question 2

When is the angle 1 radian

Answer 2

When the arc is the same length as the radius the angle is 1 (radian)

Question 3

How can you find the angle if you know the arc length?

Answer 3

angle = arc length/radius

Question 4

Calculate the angle subtended by an arc of length 8 cm with a radius of 2.5 cm

Answer 4

3.2°

Question 5

Calculate the angle subtended by an arc of length 14 cm with a radius of 30 cm

Answer 5

0.47°

Question 6

Calculate the angle subtended by an arc of length 1.4 cm with a radius of 1.8 cm

Answer 6

0.78°

Question 7

Calculate the angle subtended by an arc of length 85 cm with a radius of 15 cm

Answer 7

5.67°

Question 8

Calculate the angle subtended by an arc of length 0.64 m with a radius of 0.40 m

Answer 8

1.6°

Question 9

Calculate the angle subtended by an arc of length 26 m with a radius of 5.0 m

Answer 9

5.2°

Question 10

Calculate the angle subtended by an arc of length 5.5 m with a radius of 90 cm

Answer 10

6.1°

Question 11

Define ‘arc length’

Answer 11

Distance between 2 points on the curve

Question 12

Define ‘radius’

Answer 12

The distance between a point on the circle and the centre

Question 13

Define ‘circumference’

Answer 13

The perimeter of a circle

Question 14

Define ‘sector’

Answer 14

A slice of the circle

Question 15

Explain why an angle calculated in radians does not have any units

Answer 15

It is a ratio

Question 16

Convert these radians into degrees
1 radian
π radians
3π/4 radians
½ π radians
0.6 radians
5π radians
12.6 radians

Answer 16

60°
35°
150° 
480° 
75° 
90° 
300°

Question 17

You cut a cake into 8 equal segments through the centre. What is the angle, in radians, of the pointed end of each piece of cake?

Answer 17

0.785 rad

Question 18

A drawbridge pivots upward from the horizontal position and moves through two-thirds of the angle between the horizontal and vertical positions. Through what angle (in radians) has the drawbridge moved?

Answer 18

π/3 rad

Question 19

Cleaning up after a party, you find leftover pizza slices. The pizzas were round, and the slices were all cut through the centre. You find two slices that together make a quarter of a pizza and three slices that are each an eighth of a pizza. If you put all the slices side by side as in a pizza, what is the total angle made (in radians)?

Answer 19

3.9 rad

Question 20

The moon rotates once on its axis in about 27 days. Calculate the angle, in radians and degrees, that the moon rotates through in 1 year.

Answer 20

27π rad or 85 rad, 4900o (~13.5 rotations in 1 year)

Question 21

A CD rotates 12 600 times per minute. Calculate the angle, in radians and degrees, that a point on the CD rotates through in one minute.

Answer 21

25200π rad or 79200 rad, 4540000° (12 600 rotations in 1 minute)

Question 22

An arc subtends a central angle measuring 3π/2 radians. What fraction of the circumference is this arc?

Answer 22

0.75 or ¾ of the circumference (Arc length = 1.5π r, circumference = 2π r)

Question 23

An arc subtends a central angle measuring 80o. What fraction of the circumference is this arc?

Answer 23

0.22 of the circumference (Arc length = 0.44π r, circumference = 2π r)