A cyclist is riding a bicycle whose wheels have a radius of 12 inches. Suppose he is traveling at 15 miles per hour. (A useful fact: 1mi=5280ft. a (a) Find the angular speed of the wheels in radians per minute. (b) Find the number of revolutions the wheels make per minute. Do not round any intermediate computations, and round your answer to the nearest whole number. (a) Angular speed: square radians per minute (b) Number of revolutions per min

(a) To find the angular speed of the wheels in radians per minute, we first need to convert the linear speed from miles per hour to inches per minute.<br /><br />Given:<br />Radius of the wheel, r = 12 inches<br />Linear speed, v = 15 miles per hour<br /><br />Step 1: Convert the linear speed to feet per hour.<br />v = 15 miles/hour * 5280 feet/mile = 79200 feet/hour<br /><br />Step 2: Convert the linear speed to inches per hour.<br />v = 79200 feet/hour * 12 inches/foot = 950400 inches/hour<br /><br />Step 3: Convert the linear speed to inches per minute.<br />v = 950400 inches/hour / 60 minutes/hour = 15840 inches/minute<br /><br />Step 4: Calculate the angular speed in radians per minute.<br />Angular speed, ω = v / r<br />ω = 15840 inches/minute / 12 inches = 1320 radians/minute<br /><br />Therefore, the angular speed of the wheels is 1320 radians per minute.<br /><br />(b) To find the number of revolutions the wheels make per minute, we can use angular speed and revolutions.<br /><br />Given:<br />Angular speed, ω = 1320 radians/minute<br /><br />Step 1: Calculate the number of revolutions per minute.<br />Number of revolutions per minute = ω / 2π<br />Number of revolutions per minute = 1320 radians/minute / (2 * π)<br />Number of revolutions per minute ≈ 210.42<br /><br />Rounding to the nearest whole number, the number of revolutions the wheels make per minute is 210.