Arc Length and Angular & Linear Speed

A gear spins at a rate of 400 revolutions/minute. Which choice is closest to its angular speed in radians/second?

• 6.67 rad/s

• 2500 rad/s

• 41.9 rad/s

• 20.9 rad/s

Tags

CCSS.HSF.TF.A.1

A record spins at 33 rpm (revolutions per minute), which is an angular speed of about 3.46 radians per second. What is the approximate linear speed of a fly that sits on the record, 12 cm from the center?

• 3.4 cm/s

• 21.5 cm/s

• 41.5 cm/s

• 131.9 cm/s

Tags

CCSS.HSF.TF.A.1

CCSS.HSN.Q.A.1

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

• 90 rad/min

• 282.7 rad/min

• 45 rad/min

• 141.4 rad/min

Tags

CCSS.HSF.TF.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.HSN.Q.A.1

CCSS.HSA.REI.B.3

Determine the angular speed 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.HSF.TF.A.1

A child sits 0.75 m from the center of a merry go round. The merry go round makes one revolutions in 4 seconds. What is the child's linear speed? (Use 3.14 as pi, and Round your answer to tenths)

• 1.9 m/s

• 1.2 m/s

• 12.6 m/s

• 4.71 m/s

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.1

The wheel of a machine rotates at the rate of 300 rpm (revolutions per minute). If the diameter of the wheel is 80 cm, what is the angular speed in radian per second ?

• 1884.96 rad/sec

• 24,000 rad/sec

• 31.42 rad/sec

• 1256.29 rad/sec

Tags

CCSS.HSF.TF.A.1

The wheel of a machine rotates at the rate of 300 rpm (rotation per minute). If the diameter of the wheel is 80 cm, what is the linear speed (in cm per second) of a point on the wheel?

• 1257 cm/sec
• 200 cm/sec
• 1440,000 cm/sec
• 542 cm/sec

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.1

The length of an arc is 18cm and the radius of the circle is 6cm. What is the radian measure of the central angle?

• 3 radian

• 2 radian

• 4 radian

• 2π radian

Tags

CCSS.HSF.TF.A.1

Find the arc length.

• 3π/4 ft

• 39π/4 ft

• 13π/4 ft

• 4π/13 ft

Tags

CCSS.HSG.C.B.5