Acceleration and Rotational Motion

[Eternalmetal]

Homework Statement

If a rotational object is moving from rest to 200rpm in .23 seconds, the acceleration is?

Homework Equations

a = V^2/r
v = 2Pi(r)/t
I am sure there are others, but this is just a General Physics I course, so its dealing with Newton and Kepler's laws.

The Attempt at a Solution

To be honest, I don't know if it is totally solvable. I have a feeling that I am going to be left with a variable in my answer since the radius is not given. Without a radius, I can't figure out velocity, and without velocity I can't figure out acceleration. Judging by previous questions of my professor, the answer would most likely be in meters/second.

Working with radius as a variable, I am getting something like this:
a = (2π /.23)² r

Would this be logical, or am I going about this in the wrong way?

 

[Doc Al]

This problem is asking for angular acceleration, which is measured in radians/s^2. Angular acceleration and velocity are completely analogous to linear acceleration and velocity--the same kinematic equations apply. What's the definition of acceleration? (Be sure to convert from rpm to rad/sec.)

 

[Eternalmetal]

Ok, so 200 RPM divided by 60 is 3.3 radians/sec (correct?). Since I have the units of radians per second, I should just multiply by 1/t to get an answer in radians/sec², correct?

3.3 radians/sec * 1/.23s = 14.35 radians/sec²

Does this sound a little better then?

 

[Doc Al]

Ok, so 200 RPM divided by 60 is 3.3 radians/sec (correct?).

No. Rpm stands for revolutions per minute, not radians per minute. How many radians are in one complete revolution?

But once you get the correct value for rad/s, you have the right idea for finding the average acceleration.

 

[Eternalmetal]

Ah, if I am not mistaken, would it be 2Pi radians in one revolution? So I would multiply 3.3 revolutions/sec by 2Pi to get about 20.73 radians/sec, and then divide by .23 like I did previously and get a final value of 90.15 radians/sec² ?

Thanks for your help Doc Al.

 

[Doc Al]

Exactly right. (But carry out your intermediate calculations with a bit more accuracy. 3.3 should really be 3.3333... )

 

[Eternalmetal]

My mistake, I guess I was being a little careless. Thanks again for your help, we definitely did not go over this in lecture. Now that I realize what this is, it is a chapter that we did not cover yet, we were actually going over circular motion instead.