Arc Length and Angular and Linear Speed

The distance along an arc in linear units.

• area of a sector

• arc length

• arc measure

• segment of a circle

Find the circumference of the circle with a 7 unit radius.

• 87.82

• 153.86

• 43.96

• 307.72

If you know how fast a wheel is turning in revolutions per minute, what do you multiply by to find the angular speed?

• circumference

• π times radius

• 2π

• 360

A ceiling fan has 18 inch blades and turns at a rate of 45 revolutions per minute.  What is the angular speed in radians per hour?

• 90π rad / 1 hr
• 2700π rad / 1 hr
• 5400π rad / 1 hr
• 97200π rad / 1 hr

A car tire has a diameter of 36 cm and is spinning at 10 revolutions per second. What is the linear speed in km per hour?

• 40.72 km / 1 hr

• 50.90 km / 1 hr

• 3.28 rad / 1 hr

• 2.84 rad / 1 hr

The wheels of a car have radii of 25 cm and are rotating at 600 rotations per minute. Determine the speed of the car in km per hour to the nearest tenth.

HINT: (Determine ω (angular speed) first and then use v=ω⋅r)

• 6.3 km/hour

• 12.5 km/hour

• 56.5 km/hour

• 78.5 km/hour