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

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

Convert to radians in terms of $\pi: 200^{\circ}$

Convert to radians: 1.92 rev

A circular highway curve has a radius of $100 \mathrm{~m}$ and a central angle of $15^{\circ} 45^{\prime} 30^{\prime \prime}$ (measured to the centre line of the road). What is the length of the curve?

A capstan on a magnetic tape drive rotates at $3250 \mathrm{rad} / \mathrm{min}$ and drives the tape at a speed of 40.0 $\mathrm{m} / \mathrm{min}$ . Find the diameter of the capstan in millimetres.

Evaluate to four significant digits: $\cos \pi / 5+7 \sec \pi / 4$

A fly wheel makes 975 revolutions in one minute. How many radians does it rotate in $6.00 \mathrm{~s}$ ?

Convert to revolutions: $0.492 \mathrm{rad}$

A wheel is rotating at $134.7 \mathrm{rev} / \mathrm{min}$ . Find the linear speed of a point $15.6 \mathrm{~cm}$ from the centre.

Find the length of the arc $s$ subtended by a central angle $\theta=108^{\circ} 29^{\prime}$ of a circle of radius $r=1.73 \mathrm{~cm}$ .

Find the central angle $\theta$ of a circle of radius $r=4.000 \mathrm{~m}$ that subtends a length of arc $s=0.391 \mathrm{~m}$ .

The hour hand of a clock is $7.18 \mathrm{~cm}$ long. How far does the tip of the hand travel between 2 P.M. and 9 P.M.?

Convert to revolutions: $0.165 \mathrm{rad}$

Find the radius $r$ of a circle where a central angle $\theta=123^{\circ} 45^{\prime}$ subtends an arc length $s=9.02 \mathrm{ft}$ .

The blades on a tidal turbine turn at 17.8 revolutions per minute. How many radians does it rotate in $45.0 \mathrm{~s}$ ?

Determine the latitude of a city that is $165 \mathrm{~km}$ from the equator. Assume that the earth is a sphere with radius $6370 \mathrm{~km}$ .

Convert to radians: $37.8^{\circ}$

Evaluate to four significant digits: $\tan 2.792$

Evaluate to four significant digits: $\cot 15 \pi / 7$

A child at the edge of a spinning merry-go-round with radius 10.1 feet travels 10.0 feet in 2.0 seconds. What is the child's angular velocity in rad/sec?