Exam 16: Radian Measure, Arc Length, and Circular Motion

A $12.2 \mathrm{~m}$ long pendulum swings $4.80^{\circ}$ on each side of the vertical. Determine the length of the arc travelled by the end of the pendulum.

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Question 1

Correct Answer:

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$2.04 \mathrm{ft}$ .

Evaluate to four significant digits: $\sin^{2} \pi / 7+\csc^{2} \pi / 7$

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Question 2

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5.500

Convert to degrees: $9 \pi / 5 \mathrm{rad}$

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Question 3

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$324^{\circ}$

Evaluate to four significant digits: $\arcsin 0.871$

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Question 4

Find the central angle $\theta$ of a circle of radius $r=7.500 \mathrm{~m}$ that subtends a length of arc $s=0.755 \mathrm{~m}$ .

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Question 5

Convert to radians: $83.2^{\circ}$

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Question 6

Convert to radians in terms of $\pi: 63^{\circ}$

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Question 7

A car is travelling at a rate of $110 \mathrm{~km} / \mathrm{h}$ and has tires that have a diameter of $65 \mathrm{~cm}$ . Calculate the angular velocity ( $\mathrm{rad} / \mathrm{min})$ of the wheels of the car.

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Question 8

For peak performance, the tips of the blades on an underwater turbine should be limited to a speed of approximately $12.0 \mathrm{~m} / \mathrm{s}$ . How many revolutions per minute is this for a turbine with a diameter of $10.0 \mathrm{~m}$ ?

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Question 9

Convert to degrees (decimal): $1.069 \mathrm{rad}$

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Question 10

Find the radius $r$ of a circle where a central angle $\theta=\pi / 9$ subtends an arc length $s=21.0 \mathrm{~cm}$ .

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Question 11

Evaluate to four significant digits: $\sec^{-1} 4.50$

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Question 12

Evaluate to four significant digits: $\csc^{-1} 1.36$

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Question 13

An isosceles triangle is to be inscribed in a circle of radius $8.00 \mathrm{~cm}$ . Determine the angles of the triangle to degrees, minutes, and seconds if its base subtends an arc of length $11.34 \mathrm{~cm}$ .

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Question 14

Evaluate to four significant digits: $\sec^{2} \pi / 6+3 \cot \pi / 6$

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Question 15

Convert to degrees: $8 \pi / 7 \mathrm{rad}$

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Question 16

A gear is rotating at 25.0 revolutions per minute. How many seconds will it take to rotate through an angle of 1.00 rad?

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Question 17

Find the area of a sector with radius $6.77 \mathrm{~m}$ and central angle $70.4^{\circ}$ .

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Question 18

Find the central angle $\theta$ of a circle of radius $r=43.5 \mathrm{~cm}$ that subtends a length of arc $s=154 \mathrm{~mm}$ .

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Question 19

Convert to degrees: $3 \pi / 8 \mathrm{rad}$

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Question 20

Exam 16: Radian Measure, Arc Length, and Circular Motion

A 12.2 m12.2 \mathrm{~m}12.2 m long pendulum swings 4.80∘4.80^{\circ}4.80∘ on each side of the vertical. Determine the length of the arc travelled by the end of the pendulum.

Evaluate to four significant digits: sin⁡2π/7+csc⁡2π/7\sin^{2} \pi / 7+\csc^{2} \pi / 7sin2π/7+csc2π/7

Convert to degrees: 9π/5rad9 \pi / 5 \mathrm{rad}9π/5rad

Evaluate to four significant digits: arcsin⁡0.871\arcsin 0.871arcsin0.871

Find the central angle θ\thetaθ of a circle of radius r=7.500 mr=7.500 \mathrm{~m}r=7.500 m that subtends a length of arc s=0.755 ms=0.755 \mathrm{~m}s=0.755 m .

Convert to radians: 83.2∘83.2^{\circ}83.2∘

Convert to radians in terms of π:63∘\pi: 63^{\circ}π:63∘

A car is travelling at a rate of 110 km/h110 \mathrm{~km} / \mathrm{h}110 km/h and has tires that have a diameter of 65 cm65 \mathrm{~cm}65 cm . Calculate the angular velocity ( rad/min)\mathrm{rad} / \mathrm{min})rad/min) of the wheels of the car.

For peak performance, the tips of the blades on an underwater turbine should be limited to a speed of approximately 12.0 m/s12.0 \mathrm{~m} / \mathrm{s}12.0 m/s . How many revolutions per minute is this for a turbine with a diameter of 10.0 m10.0 \mathrm{~m}10.0 m ?

Convert to degrees (decimal): 1.069rad1.069 \mathrm{rad}1.069rad

Find the radius rrr of a circle where a central angle θ=π/9\theta=\pi / 9θ=π/9 subtends an arc length s=21.0 cms=21.0 \mathrm{~cm}s=21.0 cm .

Evaluate to four significant digits: sec⁡−14.50\sec^{-1} 4.50sec−14.50

Evaluate to four significant digits: csc⁡−11.36\csc^{-1} 1.36csc−11.36

An isosceles triangle is to be inscribed in a circle of radius 8.00 cm8.00 \mathrm{~cm}8.00 cm . Determine the angles of the triangle to degrees, minutes, and seconds if its base subtends an arc of length 11.34 cm11.34 \mathrm{~cm}11.34 cm .

Evaluate to four significant digits: sec⁡2π/6+3cot⁡π/6\sec^{2} \pi / 6+3 \cot \pi / 6sec2π/6+3cotπ/6

Convert to degrees: 8π/7rad8 \pi / 7 \mathrm{rad}8π/7rad

A gear is rotating at 25.0 revolutions per minute. How many seconds will it take to rotate through an angle of 1.00 rad?

Find the area of a sector with radius 6.77 m6.77 \mathrm{~m}6.77 m and central angle 70.4∘70.4^{\circ}70.4∘ .

Find the central angle θ\thetaθ of a circle of radius r=43.5 cmr=43.5 \mathrm{~cm}r=43.5 cm that subtends a length of arc s=154 mms=154 \mathrm{~mm}s=154 mm .

Convert to degrees: 3π/8rad3 \pi / 8 \mathrm{rad}3π/8rad

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A $12.2 \mathrm{~m}$ long pendulum swings $4.80^{\circ}$ on each side of the vertical. Determine the length of the arc travelled by the end of the pendulum.

Evaluate to four significant digits: $\sin^{2} \pi / 7+\csc^{2} \pi / 7$

Convert to degrees: $9 \pi / 5 \mathrm{rad}$

Evaluate to four significant digits: $\arcsin 0.871$

Find the central angle $\theta$ of a circle of radius $r=7.500 \mathrm{~m}$ that subtends a length of arc $s=0.755 \mathrm{~m}$ .

Convert to radians: $83.2^{\circ}$

Convert to radians in terms of $\pi: 63^{\circ}$

A car is travelling at a rate of $110 \mathrm{~km} / \mathrm{h}$ and has tires that have a diameter of $65 \mathrm{~cm}$ . Calculate the angular velocity ( $\mathrm{rad} / \mathrm{min})$ of the wheels of the car.

For peak performance, the tips of the blades on an underwater turbine should be limited to a speed of approximately $12.0 \mathrm{~m} / \mathrm{s}$ . How many revolutions per minute is this for a turbine with a diameter of $10.0 \mathrm{~m}$ ?

Convert to degrees (decimal): $1.069 \mathrm{rad}$

Find the radius $r$ of a circle where a central angle $\theta=\pi / 9$ subtends an arc length $s=21.0 \mathrm{~cm}$ .

Evaluate to four significant digits: $\sec^{-1} 4.50$

Evaluate to four significant digits: $\csc^{-1} 1.36$

An isosceles triangle is to be inscribed in a circle of radius $8.00 \mathrm{~cm}$ . Determine the angles of the triangle to degrees, minutes, and seconds if its base subtends an arc of length $11.34 \mathrm{~cm}$ .

Evaluate to four significant digits: $\sec^{2} \pi / 6+3 \cot \pi / 6$

Convert to degrees: $8 \pi / 7 \mathrm{rad}$

Find the area of a sector with radius $6.77 \mathrm{~m}$ and central angle $70.4^{\circ}$ .

Find the central angle $\theta$ of a circle of radius $r=43.5 \mathrm{~cm}$ that subtends a length of arc $s=154 \mathrm{~mm}$ .

Convert to degrees: $3 \pi / 8 \mathrm{rad}$