# Simple equation misunderstanding

Im trying to use an equation on this page

http://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics

The angle of lean, $\theta$, can easily be calculated using the laws of circular motion

$$\theta = \arctan\left(\frac{v^2}{gr}\right)$$

where $v$ is the forward speed, $r$ is the radius of the turn and $g$ is the acceleration of gravity. For example, a bike in a 10 m radius steady-state turn at 10 m/s must be at an angle of 45.6°.

If enter the above example values into the equation a get a value of 89.4 not 45.6. What am I doing wrong?

$$89.4 = \arctan\left(\frac{10^2}{9.81 \cdot 10}\right)$$

Cheers

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1
I don't know what you're doing wrong, but I'm getting a different value (in fact, the one you're looking for) for the arctan. How are you calculating it? – akkkk Dec 22 '12 at 12:30
Im entering arctan(10^2/9.81*10)*57.2957795 into google. I get 89.4379464 – user346443 Dec 22 '12 at 12:36

4
Presumably, you computed $\arctan (10^2/9.81\cdot10)$. But this was interpreted as $\arctan((10^2/9.81)\cdot 10)=\arctan(1000/9.81) \approx 89.4^\circ$. Enclose the denominator in parentheses to obtain the correct result: $\arctan(10^2/(9.81\cdot10))\approx 45.6^\circ$. – David Mitra Dec 22 '12 at 12:36
Oh ok, thanks a million and Merry Christmas. – user346443 Dec 22 '12 at 12:38
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