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

Calculate the angular velocity in revolutions per minute of a wheel that rotates at $83 \overline{0}$ radians per second.

Find the length of the arc $s$ subtended by a central angle $\theta=3 \pi / 4$ in a circle of radius $r=3.03 \mathrm{~m}$ .

Find the area of a segment of height 26.6 inches in a circle of radius 31.9 inches.

A steel bar $16.5 \mathrm{~cm}$ in diameter is being ground in a lathe. The surface speed of the bar is $16.8 \mathrm{~m} / \mathrm{min}$ . How many revolutions will the bar make in $10 \mathrm{~s}$ ?

Calculate the area of a sector with radius $12.5 \mathrm{~cm}$ and arc length of $7.24 \mathrm{~cm}$ .

Point $A$ , which is $7.50 \mathrm{~cm}$ from the centre of the airplane propeller pictured below, is travelling at 2850 $\mathrm{cm} / \mathrm{s}$ . Determine the linear speed of point $B$ which is on the same propeller and $24.5 \mathrm{~cm}$ from the centre of the propeller.

A fly wheel makes 650 revolutions in one minute. How many degrees does it rotate in $1.00 \mathrm{~s}$ ?

What arc length is subtended by a central angle of $4 \pi / 9$ in a circle of radius $145 \mathrm{~m}$ ?

Fill in the missing values.

Convert to degrees (decimal): $0.625 \mathrm{rad}$

Convert to radians in terms of $\pi: 342^{\circ}$

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

Determine the latitude of a city that is 1944 miles from the equator. Assume that the earth is a sphere with radius 3960 miles.

Convert to revolutions: $7.21 \mathrm{rad}$

A milling machine cutter has a diameter of $5.00 \mathrm{~mm}$ and is rotating at $42.5 \mathrm{rev} / \mathrm{min}$ . What is the linear speed at the edge of the cutter?

Calculate the angular velocity in degrees per second of a wheel that makes 7.5 revolutions per minute.

Evaluate to four significant digits: arccot 3.107

Fill in the missing values.

What arc length is subtended by a central angle of $76.5^{\circ}$ in a circle of radius $1.27 \mathrm{~m}$ ?

Convert to radians in terms of $\pi: 120^{\circ}$