Final answer:
To calculate wheel revolutions, first find the wheel's circumference using C = πd. Divide the total distance traveled by the circumference to determine the number of revolutions. For rate conversions, divide rev/min by 60 for rev/s, and multiply rev/s by 2π for rad/s.
Step-by-step explanation:
To calculate the revolutions of a wheel, you need to know the distance traveled and the diameter or radius of the wheel. The circumference of the wheel is given by the formula C = πd, where d is the diameter of the wheel. Once you have the circumference, you divide the distance traveled by the circumference to get the number of revolutions. For example, if a semi-trailer truck with a wheel diameter of 1.15 meters goes through 200,000 rotations, you would use the formula:
C = π × 1.15 m
Plugging in the numbers, you would calculate the circumference to be approximately 3.612 m. To find out the distance the odometer should read in kilometers, multiply the number of revolutions by the circumference and then convert meters to kilometers:
Distance traveled = 200,000 revolutions × 3.612 m/revolution = 722,400 m = 722.4 km
This is a latex free and step-by-step explanation.
For other problems like converting revolutions per minute to revolutions per second, divide the given rate by 60. As for angular velocity in radians per second, multiply the revolutions per second by 2π (since there are 2π radians in one revolution).