A wheel of a car has a radius 21 cm. If it is rotating at 800 RPM, what is the speed of the car?
The radius of the wheel is 21 cm. When the wheel rotates once, the distance covered by the car is 2*pi*21.
As the wheel rotates at 800 RPM, it covers a distance equal to 2*pi*21*800 cm per minute.
The distance covered in one hour is 2*pi*21*800*60/100 m
=> 20160*pi m
=> 20.16*pi km
=> 63.33 km (approximately)
The required speed of the car is 20.16*pi or 63.33 km/hr.
The radius r of the wheel of the car = r = 21cm.
So in one rotation of the wheel, the distance the car moves = 2pi*r = 2pi*21/100 meter.
So the distance moved by the car in 800 RPM = 2pi*21*800/100 meter.
So the speed of the car per minute = 2pi*21*800/100 = 1055.575m.
So the speed of the car per hour = 1055.576*60/1000 km
= 63.33 kilo meter/ hour.
The formula of speed when knowing the number of rotations per minute is:
s = pi*D*n/1000
D = diameter of the wheel = 2*210 = 420 mm
pi = 3.14 approx
n = 800 rpm
Now, we'll introduce the data into the formula above:
s = 3.14*420*800/1000
We'll simplify and we'll get:
s = 3.14*42*8
s = 1055.04*60 minutes
s = 63302.4
s = 63.3 Km/hour