Linear and Angular Speed

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

Tags

CCSS.HSG.C.B.5

CCSS.HSF.TF.B.5

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

• 90π ft / 1 hr

• 2700π ft / 1 hr

• 5400π ft / 1 hr

• 4050π ft / 1 hr

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

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?

• 7.95π mi / 1 hr
• 15.90 mi / 1 hr
• 3.28 rad / 1 hr
• 2.84 rad / 1 hr

Tags

CCSS.HSG.C.B.5

CCSS.HSF.TF.A.1

CCSS.HSN.Q.A.1

CCSS.HSG.GMD.A.1

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

• 120π rad / 1 hr
• 1,008,000π rad / 1 hr
• 504,000π rad / 1 hr
• 7200π rad / 1 hr

Tags

CCSS.HSG.C.B.5

CCSS.HSF.TF.A.1

A spin balancer rotates the wheel of a car at 500 revolutions per minute.  If the diameter of the wheel is 26 inches, what road speed is being tested?

• 12.31π mi / 1 hr
• 12.09π mi / 1 hr
• 13. 44π mi / 1 hr
• 24.62π mi / 1 hr

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.B.3

A spin balancer rotates the wheel of a car at 500 revolutions per minute.  If the diameter of the wheel is 26 inches, what is the angular speed in degrees per second?

• 16.67 deg / sec
• 6,000 deg / 1 sec
• 3,000 deg / 1 sec
• 180,000 deg / 1 sec

Tags

CCSS.HSG.C.B.5

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 rpm.

• 5654.9 in/min
• 1800 in/min
• 2827.4 in/min
• 900 in/min

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

• circumference

• π times radius

• 2π

• 360

Tags

CCSS.8.EE.C.7B

The wheels of a car have radius 11 in. and are rotating at 600 rpm.  Determine the speed of the car in miles/hour to the nearest tenth.  (Determine ω (angular velocity) first and then use v=ω⋅r and convert to miles/hour)

• 6.3 miles/hour
• 12.5 miles/hour
• 39.3 miles/hour
• 78.5 miles/hour

Tags

CCSS.HSN.Q.A.1

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

• 360π rad/min
• 12π rad/min
• 360 rad/min
• 720π rad/min

Tags

CCSS.8.EE.C.7B