a wheel is rotating at 30 rev/min. The angular velocity of the wheel is
a. 2pi^2 rad/s
b. 2pi rad/s
c. 2 rad/s
d. pi/2 rad/s
e. pi rad/s
explain please!
30 * 2 * pi radians / 60 seconds
thank you
To find the angular velocity of the rotating wheel, we need to know the relationship between angular velocity and the number of revolutions per minute.
Given that the wheel is rotating at 30 rev/min, we can use the conversion factor that 1 revolution is equal to 2π radians.
So, to find the angular velocity, we multiply the number of revolutions per minute by 2π.
Angular velocity = 30 rev/min * 2π rad/rev
Simplifying the expression, we have:
Angular velocity = 60π rad/min
Now, we need to convert the unit from rad per minute to rad per second. Since there are 60 seconds in a minute, we divide the angular velocity by 60.
Angular velocity = 60π rad/min / 60
Simplifying further, we get:
Angular velocity = π rad/s
Therefore, the angular velocity of the wheel is π rad/s, which corresponds to option (e).
To find the angular velocity of a rotating object, we need to determine the angle traversed by the object per unit of time. In this case, we are given that the wheel is rotating at 30 revolutions per minute.
To calculate the angular velocity, we need to convert the given information into radians and seconds. Since there are 2π radians in one revolution, we multiply the given 30 rev/min by 2π to convert it to radians per minute:
Angular velocity (in radians per minute) = 30 rev/min * 2π rad/rev = 60π rad/min.
However, we want the angular velocity in radians/second, so we must convert the time unit from minutes to seconds. There are 60 seconds in one minute, so:
Angular velocity (in radians per second) = 60π rad/min * 1 min/60 s = π rad/s.
Therefore, the correct answer is (e) π rad/s.