For this project, your solution should be written up neatly and completely on se
ID: 2883922 • Letter: F
Question
For this project, your solution should be written up neatly and completely on separate sheets of paper, with this page stapled on top. A bug is in the center of a spinning record player with a radius of 5 inches The record spins 30 times per minute. (It's a little slower than it should be. It needs to be tuned.) The bug walks in a straight line along the record to the edge at a speed of 2 inches/second. a) Using the parameter t, representing time in seconds, find parametric equations, r(t) and theta(1), for the position of the bug. b) Eliminate the parameter from part a) to find a polar coordinate equation for the path the bug travels as it walks. c) Determine the distance the bug travels from the time it leaves the center until it reaches the edge. d) Find the total distance traveled if the bug's speed is changed to 4 inches/second. What effect does this have on the total distance traveled?Explanation / Answer
Converting 30 RPM to rads / sec = 30*(2) / 60
= rad/s. This is the angular speed.
At time t, the bug walked a distance (in the frame of the disk) of "s = vt ".
Thus its distance from the center is r = vt, where v = 2 inch/s.
The angle the disc turned is = * t rad. This is thus the angle at which the bug is.
a) You now have its parametric equation in polar coords.
b) r = r()
c) The time it takes to reach the edge is found via kinematics:
s = vt --> t = s/v = 5/v seconds, with v = 2 inch/s. Thus the angle turned is (5/v) rad.
The length of the curve r() is found via the arclength formula ( r² + r'²) d, with
from 0 to (5/v).
d) Same as above but with v = 4 inch/sec...
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