# Thread: related rates: rolling wheel

1. ## related rates: rolling wheel

A wheel with radius 2 m rolls at 18 rad/s. How fast is a point on the rim of the wheel rising when the point is pi

place.)

2. Hello, drewbear!

How fast is a point on the rim of the wheel rising when the point
is $\tfrac{\pi}{3}$ radians above the horizontal and rising?
Code:
              * * *
*           *  P
*               o
*           2  *  *
*
*           * θ     *
*         o - - - - *
*         C         *

*                 *
*               *
*           *
* * *

The parametric equations of point $P$ are: . $\begin{Bmatrix}x &=& 2\cos\theta & [1] \\ y &=& 2\sin\theta & [2] \end{Bmatrix}$

$\text{We want }\,\frac{dy}{dt}\,\text{ when }\theta = \frac{\pi}{3}$

Differentiate [2] with respect to time: . $\frac{dy}{dt} \;=\;2\cos\theta\,\frac{d\theta}{dt}$

We know that: . $\cos\frac{\pi}{3} \,=\,\frac{1}{2},\;\;\frac{d\theta}{dt} \,=\,18$

Therefore: . $\frac{dy}{dt} \;=\;2\left(\tfrac{1}{2}\right)(18) \;=\;18\text{ cm/sec}$

3. thank you so much Soroban!!!