To find the linear velocity of a wheel, we need to determine the distance traveled by the wheel in a given time period.
Given: Diameter of the wheel = 80 cm Radius of the wheel = Diameter / 2 = 80 cm / 2 = 40 cm = 0.4 meters (converting to meters) Number of revolutions per minute = 120
First, we need to calculate the circumference of the wheel using the formula:
Circumference = 2 * π * radius
Circumference = 2 * π * 0.4 meters
Next, we need to calculate the distance traveled in one revolution:
Distance per revolution = Circumference
Now, we need to calculate the distance traveled in one minute (using the number of revolutions per minute):
Distance per minute = Distance per revolution * Number of revolutions per minute
Finally, we can calculate the linear velocity (speed) by dividing the distance per minute by the time in minutes:
Linear velocity = Distance per minute / Time in minutes
Let's perform the calculations:
Circumference = 2 * π * 0.4 = 2.51 meters (approx.)
Distance per revolution = Circumference = 2.51 meters
Distance per minute = Distance per revolution * Number of revolutions per minute = 2.51 meters * 120 = 301.2 meters
Time in minutes = 1 minute
Linear velocity = Distance per minute / Time in minutes = 301.2 meters / 1 minute = 301.2 meters/minute
Therefore, the linear velocity of the wheel turning at 120 revolutions per minute is approximately 301.2 meters per minute.