Solve Angular Acceleration for Blade Radius | Homework Help

[mcordi]

Homework Statement

A fan blade is rotating with a constant angular acceleration of +12.0 rad/s2. At what point on the blade, as measured from the axis of rotation, does the magnitude of the tangential acceleration equal that of the acceleration due to gravity?

Homework Equations

aT=(r)($\alpha$)

The Attempt at a Solution

What I did is rearrange the equation so that r=aT/$\alpha$
This gave me r=(9.80m/s^2)/(12.0rad/s^2)
So, r=0.0817 m/rad

The answer is supposed to be 0.817 m, but why am I getting m/rad? In fact, m/rad doesn't even make sense. Is there another way to rearrange the equation?

Any help is much appreciated. Thank you.

 

[denjay]

Radians, although a unit of measure, are dimensionless. You are getting the correct answer using a correct method.

A similar situation is in the arc length of a circle. s = rθ has the same issue where s is the arc length (meters), r is the radius (meters) and θ is the subtended angle (radians). In a circle, θ is defined by this formula as being the arc length divided by the radius. Being two distance measurements, the units cancel to be dimensionless.

We use the term radians to differentiate it from other angle measurements like degrees which are measured as being the ratio s/r = 1/360.

While looking up information that would help explain this, I found a similar question someone asked.

I suggest reading it to further your understanding of angle measurements: http://mathforum.org/library/drmath/view/64034.html