일반각과 호도법

Explain the differences between linear speed and angular speed when describing motion along a circular path.

For the following exercises, use the given information to find the length of a circular arc. Round to two decimal places.

Find the length of the arc of a circle of diameter 14 meters intercepted by the central angle of $\frac{5\pi }{6}.$

For the following exercises, use the given information to find the length of a circular arc. Round to two decimal places.

Find the length of the arc of a circle of diameter 12 meters intercepted by the central angle is $63^\circ .$

For the following exercises, use the given information to find the area of the sector. Round to four decimal places.

A sector of a circle has a central angle of $45^\circ$ and a radius 6 cm.

For the following exercises, use the given information to find the area of the sector. Round to four decimal places.

A sector of a circle has a central angle of $30^\circ$ and a radius of 20 cm.

For the following exercises, use the given information to find the area of the sector. Round to four decimal places.

A sector of a circle with diameter 10 feet and an angle of $\frac{\pi }{2}$ radians.

For the following exercises, use the given information to find the area of the sector. Round to four decimal places.

A sector of a circle with radius of 0.7 inches and an angle of $\pi$ radians.

A truck with 32-inch diameter wheels is traveling at 60 mi/h. Find the angular speed of the wheels in rad/min. How many revolutions per minute do the wheels make?

A bicycle with 24-inch diameter wheels is traveling at 15 mi/h. Find the angular speed of the wheels in rad/min. How many revolutions per minute do the wheels make?

A wheel of radius 8 inches is rotating 15°/s. What is the linear speed $v,$ the angular speed in RPM, and the angular speed in rad/s?

A wheel of radius $14$ inches is rotating $0.5$ rad/s. What is the linear speed $v,$ the angular speed in RPM, and the angular speed in deg/s?

A computer hard drive disc has diameter of 120 millimeters. When playing audio, the angular speed varies to keep the linear speed constant where the disc is being read. When reading along the outer edge of the disc, the angular speed is about 200 RPM (revolutions per minute). Find the linear speed.

When being burned in a writable CD-R drive, the angular speed of a CD is often much faster than when playing audio, but the angular speed still varies to keep the linear speed constant where the disc is being written. When writing along the outer edge of the disc, the angular speed of one drive is about 4800 RPM (revolutions per minute). Find the linear speed if the CD has diameter of 120 millimeters.

Find the distance along an arc on the surface of Earth that subtends a central angle of 5 minutes $\left(1\,\text{minute}=\frac{1}{60}\,\text{degree}\right)$. The radius of Earth is 3960 miles.

Find the distance along an arc on the surface of Earth that subtends a central angle of 7 minutes $\left(1\,\text{minute}=\frac{1}{60}\,\text{degree}\right)$. The radius of Earth is $3960$ miles.

Consider a clock with an hour hand and minute hand. What is the measure of the angle the minute hand traces in $20$ minutes?

A city is located at 40 degrees north latitude. Assume the radius of the earth is 3960 miles and the earth rotates once every 24 hours. Find the linear speed of a person who resides in this city.

A city is located at 75 degrees north latitude. Assume the radius of the earth is 3960 miles and the earth rotates once every 24 hours. Find the linear speed of a person who resides in this city.

Find the linear speed of the moon if the average distance between the earth and moon is 239,000 miles, assuming the orbit of the moon is circular and requires about 28 days. Express answer in miles per hour.

A bicycle has wheels 28 inches in diameter. A tachometer determines that the wheels are rotating at 180 RPM (revolutions per minute). Find the speed the bicycle is travelling down the road.