# Wright State University Lake Campus/2020-1/Uniform circular motion

Uses vector subtraction and similar triangles to get a=v^2/R

## Wikipedia: Centripetal force

${\displaystyle F_{c}=m_{R}\cdot a_{c}=m_{R}{\frac {v^{2}}{r}}=M_{H}\cdot g,}$

where ${\displaystyle m_{R}{\text{ and }}M_{H}}$ refer to the rotating and hanging weights respectively. You man drop the centripetal subscript "c". The following formula is not in the UNIFORM CIRCULAR MOTION handout, but will be our starting point for this lab:

${\displaystyle v\cdot T=2\pi r}$,

where T is the period, or time for one revolution. A nice way to do this experiment is to calculate speed two different ways...or you can follow the handout's procedure.

### Calculation

Now we calculate speed using two different formulas. The first formula for velocity equates the centripetal force while in motion to the tension in the string while the hanging weight is attached:

${\displaystyle {\frac {m_{R}v^{2}}{r}}=M_{H}\cdot g}$
${\displaystyle v^{2}={\frac {M_{H}}{m_{R}}}\,g\,r}$
${\displaystyle v_{H}={\sqrt {{\frac {M_{H}}{m_{R}}}gr}}}$ (based on hanging weight)
Next we calculate the velocity using a ruler to ascertain the circumference and a stopwatch to measure the period:
${\displaystyle v_{s}={\frac {2\pi r}{T}}}$ (based on stopwatch)
Consider yourself lucky if they are less than 5% apart. A quick way to get the error is to divide:
${\displaystyle {\frac {BIG}{SMALL}}=1+x}$

Loosely speaking, x yields the "percent error".

#### Graphing hanging weight versus centripetal acceleration (m_Hg versus a_c)

Copyrighted AIS/NCSU material. Here, AIS/NCSU refers Advanced Instructional Systems, Inc and North Carolina State University. The webpage https://www.yumpu.com/en/document/view/34605420/uniform-circular-motion-webassign currently offers this material if you create an account.