Centrifugal acceleration - radians^2?

In summary, the conversation discusses the use of radians in calculating centrifugal acceleration. The equations for linear and angular acceleration are mentioned, and it is explained that the radian is a dimensionless unit of angle. It is also noted that a radian is equivalent to 180 degrees.
  • #1
EinsteinKillr
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0

Homework Statement



I'm working a problem concerning centrifugal acceleration and I've stumbled on something I don't quite understand:





Homework Equations



F=mrω2 where ω=rad/s

So the resulting units: kg * m*rad2/s2


The Attempt at a Solution



I would expect acceleration to be in unit ms-2


What's up with these radians? What do they mean?
 
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  • #2
Note that there is 'linear acceleration' (i.e. rate of change of linear volocity) in m/s^2
and 'angular acceleration' (i.e. rate of change of angular velocity) in mrad/s^2 but of course radian is not an S.I. unit.
 
Last edited:
  • #3
The radian is a dimensionless quantity. It's a unit of angle (really a ratio) that has no dimension, so the final units of acceleration will be m/s2 as expected. (See: http://en.wikipedia.org/wiki/Radian#Dimensional_analysis)
 
  • #4
'radian' is a measure for an angle.
For example pi radians is equivalent to 180 degrees.
 
  • #5
Doc Al said:
The radian is a dimensionless quantity. It's a unit of angle (really a ratio) that has no dimension, so the final units of acceleration will be m/s2 as expected. (See: http://en.wikipedia.org/wiki/Radian#Dimensional_analysis)

I've never consider that a radian is a ratio of a circle. Thanks! that makes a lot more sense.
 

1. What is centrifugal acceleration?

Centrifugal acceleration is the acceleration that an object experiences when it is moving in a circular path. It is directed away from the center of the circle and can be calculated using the formula a = ω^2r, where ω is the angular velocity and r is the radius of the circle.

2. How is centrifugal acceleration different from centripetal acceleration?

Centrifugal acceleration is the outward acceleration experienced by an object moving in a circular path, while centripetal acceleration is the inward acceleration that keeps the object moving in the circular path. They are equal in magnitude but have opposite directions.

3. What is the unit of measurement for centrifugal acceleration?

The unit of measurement for centrifugal acceleration is meters per second squared (m/s^2). In the SI system, it can also be expressed in newtons (N) per kilogram (kg).

4. How does the radius affect centrifugal acceleration?

The larger the radius of the circular path, the lower the centrifugal acceleration will be. This is because as the radius increases, the object has to travel a longer distance in the same amount of time, resulting in a lower angular velocity and therefore a lower centrifugal acceleration.

5. Can centrifugal acceleration be negative?

No, centrifugal acceleration cannot be negative. It is always directed away from the center of the circle and therefore has a positive value. A negative value would indicate that the object is experiencing an acceleration towards the center, which is not possible in a purely circular motion.

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