91Ó°ÊÓ

Use the formula \(v=r \omega\) to find the value of the missing variable. $$r=12 \mathrm{m}, \omega=\frac{2 \pi}{3} \text { radians per } \mathrm{sec}$$

Use the formula \(v=r \omega\) to find the value of the missing variable. $$v=9 \mathrm{m} \text { per sec, } r=5 \mathrm{m}$$

Madison, South Dakota, and Dallas, Texas, are \(1200 \mathrm{km}\) apart and lie on the same north-south line. The latitude of Dallas is \(33^{\circ} \mathrm{N}\). What is the latitude of Madison?

Use the formula \(v=r \omega\) to find the value of the missing variable. $$r=24.93 \mathrm{cm}, \omega=0.3729 \text { radian per sec }$$

The speedometer of Terry's Honda CR-V is designed to be accurate with tires of radius 14 in. (a) Find the number of rotations of a tire in 1 hr if the car is driven at 55 mph. (b) Suppose that oversize tires of radius 16 in. are placed on the car. If the car is now driven for 1 hr with the speedometer reading 55 mph, how far has the car gone? If the speed limit is 55 mph, does Terry deserve a speeding ticket?

Find the linear speed v for each of the following. a point on the edge of a gyroscope of radius \(83 \mathrm{cm},\) rotating 680 times per min.

Earth revolves on its axis once every 24 hr. Assuming that Earth's radius is \(6400 \mathrm{km},\) find the following. (a) angular speed of Earth in radians per day and radians per hour (b) linear speed at the North Pole or South Pole (c) linear speed at Quito, Ecuador, a city on the equator (d) linear speed at Salem, Oregon (halfway from the equator to the North Pole)

A thread is being pulled off a spool at the rate of \(59.4 \mathrm{cm}\) per sec. Find the radius of the spool if it makes 152 revolutions per min.

A railroad track is laid along the arc of a circle of radius \(1800 \mathrm{ft}\). The circular part of the track subtends a central angle of \(40^{\circ} .\) How long (in seconds) will it take a point on the front of a train traveling 30.0 mph to go around this portion of the track?

The propeller of a 90 -horsepower outboard motor at full throttle rotates at exactly 5000 revolutions per min. Find the angular speed of the propeller in radians per second.