Wheel of car is making 5 revolution per second . if the diameter of the wheel is 84cm .find its speed in km/h
1 revolution = 2 pi radians
so
5 revs/sec * 2 pi radians/rev = 31.4 rad/s
which is called omega, the angular velocity
r = radius = 42 cm = .42 m
speed at rim = omega r
speed = 31.4 rad/s * .42 m = 13.2 m/s
convert now
13.2 m/s (3600 s/hr)(1 km/1000m) = 47.5 km/hr
To find the speed of the car in km/h, we first need to determine the distance traveled by the wheel in one second.
First, let's calculate the circumference of the wheel using its diameter. The formula for circumference is:
Circumference = π × diameter
Given that the diameter of the wheel is 84 cm, we can substitute this into the formula:
Circumference = π × 84 cm
Now, we need to convert the circumference from centimeters to kilometers. There are 100,000 centimeters in a kilometer. So, to convert cm to km, we divide the circumference by 100,000:
Circumference in km = Circumference in cm / 100,000
Next, let's determine the distance traveled by the wheel in one revolution, which is equal to the circumference of the wheel.
Now, we know that the wheel is making 5 revolutions per second. So, the total distance traveled by the wheel in one second is:
Total distance = Distance traveled in one revolution × Number of revolutions per second
Now, we can substitute the values into the formula:
Total distance = Circumference in km × Number of revolutions per second
Finally, to find the speed of the car in km/h, we need to convert the total distance traveled in one second to kilometers per hour. There are 3600 seconds in an hour. So, to convert seconds to hours, we multiply the total distance by 3600:
Speed in km/h = Total distance × 3600
By following these steps, we can find the speed of the car in km/h.