Chapter 14

Convert 1850 rev/min to radians per second and degrees per second.

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). \(r=4.83\) in., \(\theta=2 \pi / 5 . \quad\) Find \(s\)

Convert to radians. $$47.8^{\circ}$$

Convert 5.85 rad/s to revolutions per minute and degrees per second.

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). \(r=11.5 \mathrm{cm}, \theta=1.36 \mathrm{rad} .\) Find \(s\).

Convert to radians. $$18.7^{\circ}$$

Convert 77.2 deg/s to revolutions per minute and radians per second.

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). \(r=284 \mathrm{ft}, \quad \theta=46.4^{\circ}\) Find \(s\).

Convert to radians. $$35.25^{\circ}$$

Convert \(3 \pi / 5\) rad/s to revolutions per minute and degrees per second.

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). \(r=2.87 \mathrm{m}, \quad \theta=1.55 \mathrm{rad} . \quad\) Find \(s\).

Convert to radians. 0.370 rev

Convert 48.1 deg/s to revolutions per minute and radians per second.

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). \(r=64.8\) in. \(\theta=38.5^{\circ} . \quad\) Find \(s\).

Convert to radians. 1.55 rev

Convert 22,600 rev/min to radians per second and degrees per second.

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). \(r=28.3 \mathrm{ft}, \quad s=32.5 \mathrm{ft} . \quad\) Find \(\theta\).

Convert to radians. 1.27 rev

A disk is rotating at 334 rev/min. Find the linear speed, in \(\mathrm{ft} / \mathrm{min}\), of a point 3.55 in. from the center.

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). \(r=263 \mathrm{mm}, s=582 \mathrm{mm} .\) Find \(\theta\).

Convert to revolutions. $$1.75 \mathrm{rad}$$

A wheel rotates at 46.8 rad/s. Find the linear speed, in \(\mathrm{cm} / \mathrm{s}\), of a point 36.8 cm from the center.

Convert to revolutions. $$2.30 \mathrm{rad}$$

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). \(r=21.5 \mathrm{ft}, \quad s=18.2 \mathrm{ft} . \quad\) Find \(\theta\).

Convert to revolutions. 3.12 rad

Convert to revolutions. $$0.0633 \mathrm{rad}$$

The rim of a rotating wheel \(83.4 \mathrm{cm}\) in diameter has a linear speed of 58.3 m/min. Find the angular velocity of the wheel in rev/min.

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). $$ \theta=\pi / 12, \quad s=88.1 \text { in. Find } r $$.

Convert to revolutions. $$1.12 \mathrm{rad}$$

A flywheel makes 725 revolutions in a minute. How many degrees does it rotate in \(1.00 \mathrm{s} ?\)

Convert to revolutions. $$0.766 \mathrm{rad}$$

A propeller on a wind generator rotates \(60.0^{\circ}\) in 1.00 s. Find the angular velocity of the propeller in revolutions per minute.

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). \(\theta=2.08 \mathrm{rad}, s=3.84 \mathrm{m} . \quad\) Find \(r\)

Convert to degrees (decimal). $$2.83 \mathrm{rad}$$

A gear is rotating at 2550 rev/min. How many seconds will it take to rotate through an angle of 2.00 rad?

Convert to degrees (decimal). $$4.275 \mathrm{rad}$$

A sprocket 3.00 inches in diameter is driven by a chain that moves at a speed of 55.5 in./s. Find the angular velocity of the sprocket in rev/min.

In the following exercises, \(s\) is the length of are subtended by a central angle \(\theta\) in a circle of radius \(r\). \(\theta=5 \pi / 6, \quad s=125 \mathrm{mm} . \quad\) Find \(r\)

Convert to degrees (decimal). 0.372 rad

Where needed, assume the earth to be a sphere with a radius of 3960 mi. Actually, the distance from pole to pole is about 27 mi less than the diameter at the equator. A certain town is at a latitude of \(35.2^{\circ} \mathrm{N} .\) Find the distance in miles from the town to the north pole.

Convert to degrees (decimal). $$0.236 \mathrm{rad}$$

A blade on a water turbine turns \(155^{\circ}\) in 1.25 s. Find the linear speed of a point on the tip of the blade 0.750 m from the axis of rotation.

Where needed, assume the earth to be a sphere with a radius of 3960 mi. Actually, the distance from pole to pole is about 27 mi less than the diameter at the equator. Find the latitude of a city that is 1265 mi from the equator.

Convert to degrees (decimal). $$1.14 \mathrm{rad}$$

A steel bar 6.50 inches in diameter is being turned in a lathe. The surface speed of the bar is \(55.0 \mathrm{ft} / \mathrm{min} .\) How many revolutions will the bar make in \(10.0 \mathrm{s} ?\)

Assuming the earth to be a sphere 7920 mi in diameter, calculate the linear speed in miles per hour of a point on the equator due to the rotation of the earth about its axis.

Convert to degrees (decimal). $$0.116 \mathrm{rad}$$

Where needed, assume the earth to be a sphere with a radius of 3960 mi. Actually, the distance from pole to pole is about 27 mi less than the diameter at the equator. City \(B\) is due north of city \(A\). City \(A\) has a latitude of \(14^{\circ} 37^{\prime} \mathrm{N},\) and city \(B\) has a latitude of \(47^{\circ} 12^{\prime} \mathrm{N}\). Find the distance in kilometers between the cities.

Assuming the earth's orbit about the sun to be a circle with a radius of \(93.0 \times 10^{6} \mathrm{mi},\) calculate the linear speed of the earth around the sun.

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$60^{\circ}$$