# How Do You Convert Angular Velocity to RPM?

• blackice552
In summary, the conversation discusses finding the angular velocity in rpm's at t=2s for a circular path with a radius of 30 cm. The equation used is omega=d theta/dt and the calculated value at t=2s is 42 rad/s. The concept of rpm is explained as rounds per minute and it is determined by dividing the angular speed by 2pi, as 2pi is equivalent to one round. The radius of 30 cm is not relevant in calculating rpm.
blackice552
1. Homework Statement
theta(t) = 2t^3 + 5t^2 - 2t + 1

Find the angular velocity in rpm's at t = 2s if the radius of the circular path is 30 cm

Basically I want to kno if i did this part of the problem right b/c my professor didn't give us a key for the practice exam

2. Homework Equations
omega = d theta/dt

3. The attempt at a solutio
omega(t) = 6t^2 + 10t -2
omega(2) =42 m/s
30 cm = .3 m
Circumference = .3(2)pi = .6pi
42 m/s * 60s/min = 252 m/min
252 m/min * 1 rev/.6pi m = 42/pi rpm

omega(2) = 42 (deg or rad)/s depends on the unit used..
if you have the the angular velocity all you need to find how much rpm: is to divide 2*pi by omega(to find out how much it takes to make a full turn aka 2*pi) and then see how many round in one minute..
Edit:Btw it's either 2*pi or 360 depends on unit used..

Last edited:

Did you understand what I said?
do you need me to explain more?

could u please explain a little more

you have calculated that at t=2 the angular speed is 42 rad/s
you know that rpm means round per minute.
a round is equivalent to what? it's equivalent to a full trip around that circle, that means it must goes through a 2*pi(360 degree) trip to return from where it started.
now since you know the angular speed, and you know the angle 2*pi, you can calculate how much time is needed to make that trip..
hence you can calculate how many trips can be done in one minute, if you know how much time is needed to make one round

so the radius of 30 cm has nothing to do with it? I thought the circumference would be the round

you have the angular speed , not the linear speed, you know how much the angle is changing per second , not how much distance per second(although it's easy to calculate it)
I thought the circumference would be the round
so? unless you want to use the linear speed , the circumference have no use to calculate the rpm..
what part you need more explaining?

i think i understand now so intead of dividing by the circumference like i was doing all i have to do is divide by 2 pi

yes divide the angular speed by 2pi to calculate how much time does it need to turn 2pi which is equivalent to one round...

thanks for the help

## 1. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating about a fixed axis. It is typically represented by the Greek letter omega (ω) and is measured in radians per second (rad/s).

## 2. How is angular velocity related to rpm?

Rpm (revolutions per minute) is a unit of rotational speed commonly used in everyday life. Angular velocity and rpm are related by a conversion factor of 60 seconds per minute, meaning that 1 rpm is equal to π/30 rad/s.

## 3. What is the formula for converting angular velocity to rpm?

The formula for converting angular velocity (ω) to rpm is: rpm = ω * 60 / 2π. This formula is derived from the conversion factor of 60 seconds per minute and the fact that there are 2π radians in a full rotation (360 degrees).

## 4. Can angular velocity be negative?

Yes, angular velocity can be negative. A negative angular velocity means that the object is rotating in the opposite direction of a positive angular velocity (counterclockwise instead of clockwise).

## 5. How is angular velocity measured?

Angular velocity can be measured using a variety of tools such as a tachometer, stroboscope, or accelerometer. These devices measure the rotation of an object and calculate the angular velocity based on the time it takes to complete one full rotation.

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