Chapter 6

Speed at the Equator The earth rotates about its axis once every 23 \(\mathrm{h} 56 \mathrm{min} 4 \mathrm{s}\) , and the radius of the earth is 3960 \(\mathrm{mi}\) . Find the linear speed of a point on the equator in mi/h.

Truck Wheels A truck with 48 -in.-diameter wheels is traveling at 50 \(\mathrm{mi} / \mathrm{h}\) . (a) Find the angular speed of the wheels in rad/min. (b) How many revolutions per minute do the wheels make?

Speed of a Current To measure the speed of a current, scientists place a paddle wheel in the stream and observe the rate at which it rotates. If the paddle wheel has radius 0.20 \(\mathrm{m}\) and rotates at \(100 \mathrm{rpm},\) find the speed of the current in \(\mathrm{m} / \mathrm{s}\) .

Bicycle Wheel The sprockets and chain of a bicycle are shown in the figure. The pedal sprocket has a radius of 4 in. the wheel sprocket a radius of 2 in. and the wheel a radius of 13 in. The cyclist pedals at 40 \(\mathrm{rpm}\) . (a) Find the angular speed of the wheel sprocket. (b) Find the speed of the bicycle. (Assume that the wheel turns at the same rate as the wheel sprocket.)

Different Ways of Measuring Angles The custom of measuring angles using degrees, with \(360^{\circ}\) in a circle, dates back to the ancient Babylonians, who used a number system based on groups of \(60 .\) Another system of measuring angles divides the circle into 400 units, called grads. In this system a right angle is circle into 400 units, called grads. In this system a right angle is 100 grad, so this fits in with our base 10 number system. Write a short essay comparing the advantages and disadvantages of these two systems and the radian system of measuring angles. Which system do you prefer? Why?

Clocks and Angles In one hour, the minute hand on a clock moves through a complete circle, and the hour hand moves through \(\frac{1}{12}\) of a circle. Through how many radians do the minute and the hour hand move between \(1 : 00\) P.M. and \(6 : 45\) P.M. (on the same day)?