If a tire rotates 150 revs/min when a truck is travelling 40km/h, what is the circumference of the tire?
Given that the tire rotates 150 revs/ min
Also, given that the truck is traveling 40 km / h
First we will determine how many m / min the truck travels:
(40km/h) x (h/60min) = (2/3)km/min
==> We know that :
1 km = 1000m
==> (2/3) km / min = (2000/3) m / min
Now we will calculate the circumference of the tire:
Let x be the circumference of the tire:
(150revs/min) (x m/rev) = 2000/3 m/min
150x = 2000/3 m/min
x m = 2000/450 = 4.4
x = 4.4 meters
Then the circumference of the tire is 4.4 m
Speed of truck = 40 km/H = 40*1000 = 40,000 m/h
Rotational speed of tire = 150 rev/min = 150*60 = 9,000 rev/h
For each rotation of a tire the truck moves by a distance equal to the circumference of the tire.
Therefore the circumference of the tire is equal to:
Circumference = (Speed of truck)/(Rotational speed of tires)
Substituting the given values of speed of truck and rotational speed of tires in the above equation:
Circumference = 40,000/9,000 = 4.4444 m
Circumference of tire = 4.4444 m.
The number of rotations of the tyre per minute = 150 reveloutions/ minute.
The speed of the truck = 40km/hour.
Therefore the distance covered by the truck per minute = 40 km /60 min = 40000m/60 = 2000/3 m . Therefore the wheel moves by 2000/3 m in 150 revlutions.
Therefore the in one revolution the wheel moves by a distance (2000/3)/150 m = 40/9 meter = 4.44 meter.
Since the distance moved by one rotation of the wheel is equal to the circumference, 4.4m is circumference of the wheel.