Find the speed of a point on the rim of a 24cm diameter fly wheel which is turning at 2800 revolutions per minute. Give your answer in meters per second.
2800 rev/min * 24πcm/rev = 67200π cm/min
I'm sure you can convert that to m/s
To find the speed of a point on the rim of a flywheel, we need to convert the revolutions per minute (rpm) to radians per second and then multiply it by the radius of the flywheel.
1. Find the angular velocity in radians per second:
- Given the flywheel is turning at 2800 revolutions per minute, we need to convert it to radians per second.
- 1 revolution = 2π radians
- Thus, 2800 revolutions = 2800 * 2π radians
- To convert minutes to seconds, we multiply by 60: (2800 * 2π * 60) radians per minute
2. Convert radians per minute to radians per second:
- To convert from minutes to seconds, we divide by 60: (2800 * 2π * 60) / 60 radians per second
3. Find the radius of the flywheel:
- Given that the diameter is 24 cm, the radius is half of the diameter.
- Radius = 24 cm / 2 = 12 cm
- Since the answer should be in meters per second, we need to convert cm to meters: 12 cm = 0.12 meters
4. Calculate the speed of a point on the rim:
- Multiply the angular velocity by the radius: (2800 * 2π * 60) / 60 * 0.12 meters per second
Performing the calculations, the speed of a point on the rim of the flywheel is approximately 329.867 meters per second.
To find the speed of a point on the rim of a flywheel, we need to know the diameter of the flywheel and the number of revolutions per minute.
1. First, convert the diameter from centimeters to meters:
Diameter = 24 cm = 24/100 m = 0.24 m
2. Next, we need to calculate the circumference of the flywheel using the formula:
Circumference = π * Diameter
Since π is a constant with a value of approximately 3.14159, we can plug in the values:
Circumference = 3.14159 * 0.24 m
Calculate the circumference: Circumference = 0.7539824 m
3. Now, we can find the distance covered by the point on the rim in one revolution by using the circumference:
Distance covered in one revolution = Circumference
Distance covered in one revolution = 0.7539824 m
4. Finally, we can find the speed of the point on the rim by multiplying the distance covered in one revolution by the number of revolutions per minute and converting the result to seconds:
Speed = (Distance covered in one revolution * Revolutions per minute) / 60
Speed = (0.7539824 m * 2800) / 60
Calculate the speed: Speed ≈ 35.146 m/s
Therefore, the speed of a point on the rim of a 24 cm diameter flywheel, turning at 2800 revolutions per minute, is approximately 35.146 meters per second.