# $\pi$ radians per second for velocity

I have a question that I need clarifying. To calculate the final angular velocity from initial angular velocity, angular acceleration and time I would do $V_{f} = V_{i} + a * t$. this seems relatively straight forward however I have been given these values and i'm not sure how to work with them properly.

$V_{i}$ = $\pi$ rad/s

$a$ = $2\pi$ rad/$s^{2}$

$t$ = $10$s

What would be a solution to working with $\pi$ radians to find the final velocity?

• Welcome to MSE! It really helps readability to format questions using MathJax (see FAQ). Regards – Amzoti Apr 26 '13 at 0:11

You seem to have the right idea from the equation you posted, so I'm not sure what part of the process you're getting stuck on. I'll post a solution and maybe you can clarify what parts are difficult for you.

$V_{f} = V_{i} + a*t$ for constant acceleration $a$. Since all of our units are already consistent, i.e., the initial velocity is given in radians per second, the time elapsed is given in seconds, and the acceleration is given in radians per second squared, we simply plug in and evaluate. We find: $V_{f} = \pi \text{ rad/s} + 2\pi \text{ rad/}s^{2}*10\text{s} = 21\pi \text{ rad/s}$.

• My knowledge in radians is limited so say i have the same question using the same equation but instead of π rad/s i have π/4 rad/s + π/4 rad/s2 * 10s. How would you solve this. Is 2π the same as π/2? – Robbie Apr 26 '13 at 1:10

If you use this formula with these units, it will give you an answer with the same units (i.e. $rad.s^{-1}$).

pi here is not part of the unit, it is the measurement : at $t=0$, your object is making one half-turn every second.

• Thank you pkr! very much appreciated for the response. – Robbie Apr 26 '13 at 0:29

$V_f=\pi rad/s+2 \pi 10 s. rad/s^2=21 \pi rad/s$

$\pi$ is the number, so you can leave the answer as that (best option) or use $21\pi=65.9734...$ (more "messy" option)

• Thank you very much for the answer. – Robbie Apr 26 '13 at 0:28