If a flywheel 8 ft. in diameter rotates at 80 rpm., what is the linear velocity of a point on the outside edge, in feet per minute in terms of pi?
C = πd = 8π feet. So, the linear speed around the edge is
8π ft * 80/min = 640π ft/min
To find the linear velocity of a point on the outside edge of a rotating flywheel, we need to use the formula:
Linear velocity = (Angular velocity) x (Radius)
The angular velocity is given as 80 rpm. To convert this to radians per minute, we need to multiply it by 2π radians (since there are 2π radians in a full revolution):
Angular velocity = 80 rpm x 2π radians/minute = 160π radians/minute
The radius is half the diameter, so in this case, it's 8 ft. ÷ 2 = 4 ft.
Therefore, the linear velocity in feet per minute can be calculated by multiplying the angular velocity by the radius:
Linear velocity = (160π radians/minute) x (4 ft) = 640π ft/minute
So, the linear velocity of a point on the outside edge of the flywheel in terms of pi is 640π ft/minute.