Determine the polar equation that gives the distanve from the center of the record to the needle on a 12" LP as a function of the total angle the record has spun. You are to use the following facts about record players:

The diameter of the record is 12", which is where the needle starts. The center sticker is 5" in diameter, and the needle stops at the outer edge of this sticker. The record spins at thirty three and one third revolutions per minute. The audio content of one side of the record is 20 minutes in length.

Question

Determine the polar equation that gives the distanve from the center of the record to the needle on a 12" LP as a function of the total angle the record has spun.  You are to use the following facts about record players:

The diameter of the record is 12", which is where the needle starts.  The center sticker is 5" in diameter, and the needle stops at the outer edge of this sticker.  The record spins at thirty three and one third revolutions per minute.  The audio content of one side of the record is 20 minutes in length.

anonymous · Answer

r=(-1.6711e-3 in)theta+12 in

anonymous · Answer

can you explain how you got there?  I am not seeing it and it is really the process that I need to learn.

Thanks!

anonymous · Answer

What have you done so far?

anonymous · Answer

First of all, we know that the record spins at a rate of 33 1/3 revs/min, and that the record lasts for twenty minutes, you can multiply them together to find that the record spins a total of 666 2/3 revolutions.

anonymous · Answer

this s the first time i have encountered "polar equations".  I am not really sure what form that type of equation takes.  

If the record is 12" in diameter and the sticker is 5" in diameter, then there are 3.5 inchs that the needle moves over.

If the record is moving at 33.3 revolutions per minute and it revolves for 20 minutes then I know that there are 666 & 2/3  revolutions to be made over that 3.5 inches.  This would also be thought ofas approx. 240000 degrees.  

$$\Theta/240000 = distance/3.5$$

which can be rearranged as a function of degrees as $$(3.5\Theta)/240000$$
where Theta is is degrees

anonymous · Answer

In polar equations, your input is theta, and your output in r, radius. Because the needle moves closer to the center at a constant rate, this particular equation acts exactly like a straight line. You can think of theta as your x axis, and r as your y axis.

anonymous · Answer

If you think of it like this, the graph would be a straight line. The graph of this function graphed in polar coordinates would look the same as the path the needle takes over the surface of the record.

anonymous · Answer

The answer I gave you is in radians, by the way.

anonymous · Answer

this i starting to make more sense....but I am not quite with you.  where did the e come from?  how exactlyl did you arrive at that equation?

anonymous · Answer

the e is for scientific notation, it would be negative 1.6711*10^-3. This number is the slope of the line in inches/radians.