Question

A car tire has a radius of 1.5 feet. If the tire is rotating at 800 rpm, what is the speed of the car in miles per hour (1 mile = 5,280 feet)? Round the answer to the nearest tenth.

Answer 1

The first the is to find the distance covered when the wheel makes one rotation.

circumference = 2π×1.5=9.424778 feet

In one minute the car would cover (9.424778×800)= 7,539.822369 feet

Speed = distance/time
time = 1 minute = (1/60) hours
distance = (7,539.822369/5280)=1.427996661 miles

∴ speed = 1.427996661÷(1/60)
= 85.7 miles per hour

Answer 2

Radius = r = 1.5 feet

Angular velocity = w = 800 rpm = 800 revolutions per minute
Angular velocity = w = 800 x 2π radians per minute

w = 1600π radians per minute

Linear velocity = speed = v =r w

So,

v = 1.5 x 1600π feet per minute

v = 2400π feet per minute

v = 2400π x 60/5280 miles per hour

v = 85.7 miles per hour

So, the speed of the car is 85.7 miles per hour