(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 1.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as

θ =2.50t^{2}- 0.600t^{3}

where θ is in radians andtis in seconds. (a) Find the maximum angular speed of the roller. (b) What is the maximum tangential speed of a point on the rim of the roller? (c) At what time t should the driving force be removed from the roller so that the roller does not reverse its direction of rotation? (d) Through how many rotations has the roller turned between t=0 and the time found in part (c)?

2. Relevant equations

I think this has to do with translational and angular quantities. a_{c}=v^{2}/r=rω² might be useful.

For part b, a_{t}=rα

3. The attempt at a solution

I took the derivative of the rotational position to get angular speed in terms of t. I know the radius is .5 m. I don't understand how a max speed can be reached, as it would increase indefinitely with time. I don't think I'm grasping the problem. I also don't understand how the roller could reverse its direction. Any help is much appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Find Maximum Angular Speed

**Physics Forums | Science Articles, Homework Help, Discussion**