Linear Angular Velocity

Calculate the length of an arc with radius 15 cm and central angle of 30°.

• 450 cm
• 5π/2 cm or ≈ 7.9 cm
• 225 cm
• 5π/4 cm or ≈ 3.9 cm

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

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

Find the angle generated by point P in time when r = 20 cm, w=pi/12 per sec and t = 6 sec.

• Pi/2

• pi

• pi/12

• 6

Find the linear speed of P when r = 30 cm, w= pi/10 per sec and t = 4 sec.

• pi/10

• 2 pi

• 3 pi

• pi/2

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

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.HSA.CED.A.1

CCSS.HSA.CED.A.4

CCSS.HSN.Q.A.1