# Angular Speed

• Feb 22nd 2010, 01:42 PM
MJ320
Angular Speed
Hi everyone... new to the forum but I've read posts before that have helped me out a lot.

A patrol car is parked 50' from a long warehouse. The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write theta as a function of x. How fast is the light beam moving along the wall when the beam makes an angle of theta = 45 degrees with the line perpendicular from the light to the wall.

I'm kind of lost as to where to even start here. I know I'm looking for dx/dt.

do I start by saying tan(theta) = x/50
theta = [arctan](x/50)

then differentiate that dtheta/dt (which is 30) = d/dx [arctan](x/50)

u = (x/50) so u' = 1/50

30 = (1/50)/[1+(x/50)^2]

Trying to see if I'm on the right path here, and if so, what is the next step. Any help would be greatly appreciated.

Thanks,
MJ
• Feb 22nd 2010, 04:33 PM
skeeter
Quote:

Originally Posted by MJ320
Hi everyone... new to the forum but I've read posts before that have helped me out a lot.

A patrol car is parked 50' from a long warehouse. The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write theta as a function of x. How fast is the light beam moving along the wall when the beam makes an angle of theta = 45 degrees with the line perpendicular from the light to the wall.

I'm kind of lost as to where to even start here. I know I'm looking for dx/dt.

do I start by saying tan(theta) = x/50
theta = [arctan](x/50)

then differentiate that dtheta/dt (which is 30) = d/dx [arctan](x/50)

u = (x/50) so u' = 1/50

30 = (1/50)/[1+(x/50)^2]

Trying to see if I'm on the right path here, and if so, what is the next step. Any help would be greatly appreciated.

Thanks,
MJ

everything is ok except for $\frac{d\theta}{dt}$ ... you have to convert 30 rpm to units of rad/min.

$\frac{dx}{dt}$ will be in ft/min
• Feb 22nd 2010, 08:07 PM
MJ320
Awesome. I had actually thought about that too, but wanted to at least make sure I was on the right path. Thanks.