Doris H. answered • 02/10/25
Experience Math Specialist: Helping Students to Improve Math Scores
A wheel spins through 31 revolutions per minute. Find the angular velocity and the linear velocity if the radius of the wheel is 1.7 feet.
Solving for the following: angular velocity and linear velociy of a spinning wheel.
Information given:
The wheel spins at 31 revolutions per minute.
The radius of the wheel is 1.7 ft.
Notes: 1 revolution = 2 pi radians
Definitions:
Angular velocity is the time rate which an object rotates.
Linear velocity is the speed of an object moving in a straight line.
Formula: Linear velocity (v) used for (circular motion) v = rw r = radius of circle (wheel) w=omega
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Angular velocity measurement (units) conversion
Convert revolutions to radians: 31 revolutions = 31 x 2pi radians = 62pi radians = 62pi radians per minute
Convert minutes to seconds : 1 minute = 60 seconds
angular velocity = 62 pi / 60 radians per second = 31pi / 30 radians per second
(Simplify divide by 2)
Calculate the linear velocity (v) v=rw r = radius of the wheel is 1.7 ft
w= angular velocity = 31pi /30 radians per second
Use linear velocity (v) formula:
v=rw
v = 1.7 x 31pi / 30 feet per second = 1.7 x 3.246312409= 5.518731095 = 5.52 feet per second
v = 5.52 feet per second
Solutions:
The angular velocity 31pi / 30 radians per second
The linear velocity is 5.52 feet per second
I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.