Free Printable Arc Length, Angular and Linear Velocity wp

1.

Which of the following can be used to calculate the circumference of a circle? (SELECT ALL THAT APPLY)

a)

$C=2\pi r$

b)

$C=\pi r^2$

c)

$A\ =\ \pi r^2$

d)

$C=\pi d$

2.

Calculate the circumference, $2\pi r$ , of the circle. (Leave answers in terms of $\pi$ . Do not round your answer.)

a)

$4\pi$ m

b)

$1\pi$ m

c)

$2\pi$ m

3.

Calculate the circumference, $2\pi r$ , of of the circle. (Leave answers in terms of $\pi$ . Do not round your answer.)

a)

$3\pi$ yd

b)

$12\pi$ yd

c)

$6\pi$ yd

4.

Which of the following formulas calculates the arc length of a circle? (Select ALL that apply.)

a)

$\frac{\theta}{180}\times2\pi r$

b)

$\frac{\theta}{360}\times2\pi r$

c)

$\frac{\theta}{360}\times\pi d$

d)

$\frac{\theta}{360}\times\pi r^2$

5.

Find the arc length of the circle. (Leave answers in terms of $\pi$ . Do not round your answer.)

a)

$27\pi$ km

b)

$\frac{\pi}{18}$ km

c)

$15\pi$ km

d)

$\frac{15\pi}{2}$

6.

The formula for the arc length given an angle measurement in radians is

a)

$2\pi r\theta$

b)

$r^2$

c)

$r\theta$

7.

Find the arc length indicated by the bolded arc.

a)

8.4 mi

b)

9.4 mi

c)

60.2 mi

d)

117.8 mi

8.

Find the arc length indicated by the bolded arc.

a)

17.3 km

b)

79.1 km

c)

95.0 km

d)

99.0 km

9.

Find the arc length indicated by the bolded arc.

(answer in terms of pi)

10.

A ceiling fan with 16 inch blades rotates at 45 revolutions per minute. Find the angular velocity of the fan in rad/min. Round to the nearest tenth.

a)

90 rad/min

b)

282.7 rad/min

c)

45 rad/min

d)

141.4

11.

Determine the angular velocity in rad/min of a gyroscope rotating at 6 rps (revolutions per second). Leave answer in terms of π.

a)

360π rad/min

b)

12π rad/min

c)

360 rad/min

d)

720π rad/min

12.

Choose all that are equivalent

a)

$\pi$

b)

$2\pi$ radians

c)

one revolution

d)

$360\degree$

e)

1 radian

13.

A car tire has a diameter of 14 inches and is spinning at a of 10 revolutions per second. What is the linear speed in miles per hour?

a)

7.95π mi / 1 hr

b)

15.90 mi / 1 hr

c)

3.28 rad / 1 hr

d)

2.84 rad / 1 hr

14.

What are the units of angular velocity?

a)

radians per second (rad/s)

b)

seconds per meter (s/m)

c)

kilograms per second (kg/s)

d)

meters per second (m/s)

15.

Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20 inch blades rotating at 45 revolutions per minute.

a)

5654.9 in/min

b)

1800 in/min

c)

2827.4 in/min

d)

900 in/min

Arc Length, Angular and Linear Velocity wp

Total questions: 15

Worksheet time: 35mins

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