Angular and Linear Velocity

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

• 90 rad/min
• 282.7 rad/min
• 45 rad/min
• 141.4

Tags

CCSS.HSF.TF.A.1

CCSS.HSN.Q.A.1

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

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.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

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.HSF.TF.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.HSA.SSE.A.1

CCSS.HSG.GMD.A.1

CCSS.HSN.Q.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.HSA.SSE.A.1

CCSS.HSF.TF.A.1

CCSS.HSG.GMD.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.A.1

CCSS.HSG.GMD.A.1

CCSS.HSN.Q.A.1

A grindstone spinning at the rate of 8.3 rev/s has what approximate angular speed?

• 3.2 rad/s
• 26 rad/s
• 52 rad/s
• 81 rad/s

Tags

CCSS.HSF.TF.A.1

CCSS.HSG.C.B.5

CCSS.HSN.Q.A.1

Two bugs ride a turntable which is rotating at a constant rate of 4 rad/s. Bug A is at a radius of 4 cm, while bug B is at a radius of 8 cm. Which of the following is true? 

• Bug A has a greater rotational speed. 
• Bug B has a greater rotational speed. 
• Bug A has a greater speed. 
• Bug B has a greater speed. 

Which has greater angular speed, a horse near the outside rail of a merry-go-round or a horse near the inside rail?

• The inside horse
• The outside horse
• Neither - they both have the same angular speed

Tags

CCSS.HSG.C.B.5