Non-Linear Parametric motion help!!

ascofield33 · 2014-03-03 14:09:49

In the diagram below, a pulley with 5-cm radius is centered at O(0,0). A second pulley with 2-cm radius is centered at B(10,0). The pulley at O is rotating counterclockwise at 2 revolutions per second.
a.) Find the angular velocity of the pulley with center at point B.
Wouldn't both pulleys have the same angular velocity of 2?
b.) Write parametric equations that model the position of point A as the pulley rotates around its center O starting at point (5,0).
I said x=5cos2T and y=5sin2T
c.) Model the position of point C with parametric equations, if its starting position is (12,0).
I said x=2cos2T and y=2sin2T + 10
d.) Enter the algebraic description of both circles, and display the graphs using Simul mode.
e.) Set Tmin and Tmax so that one revolution around the circle with center O is graphed. What happens to the graph of the related motion around the circle with center B? Explain.
I said the graph of the motion of the circle with center B also shows one revolution because it is going at the same speed.
f.) Set Tmin and Tmax so that one revolution around the circle with center B is graphed. What happens to the graph of the related motion around the circle with center O? Explain.
I said the graph of the motion of the circle with center O also shows one revolution because it is going at the same speed.

I wanted to make sure my answers are correct because I have a feeling that they're not because I don't think the answers for e and f should basically be the same...

bobbym · 2014-03-03 16:07:48

Hi ascofield33;

Please provide the link to the diagram.

ascofield33 · 2014-03-03 17:11:48

This is the only way I can figure out how to show you the diagram.

https://www.google.com/search?q=core+plus+mathematics+course+4&sourceid=ie7&rls=com.microsoft:en-US:IE-Address&ie=&oe=#q=suppose+your+dart+throwing+opponent+is+most+accurate+when+he+throws+at+an+initial+velocity&rls=com.microsoft:en-US:IE-Address

Click on the 3rd link (it should be a PDF). And on the PDF, it is on page 70. (#5).

Last edited by ascofield33 (2014-03-03 17:15:05)

Bob · 2014-03-03 20:15:30

hi ascofield33

Welcome to the forum.

Diagram below.

(a) The angular velocities are not the same.

When the larger pulley, radius 5, rotates once it winds on a length of 2 x 5 x pi of the drive belt.

The smaller pulley, radius 2, will rotate once each time a length of 2 x 2 x pi goes around it.

So number of revolutions of the smaller pulley for one of the larger is (2 x 5 x pi)/(2 x 2 x pi) = 5/2

So (revs of smaller) is (revs of larger) x 5/2 = 5rps.

If you've got a bicycle handy get someone to lift up the rear wheel and try it with one turn of the pedals. How many times does the rear wheel go round?

(b)

You have the right idea with these equations, but what is T ?

The larger pulley takes 2 seconds to rotate once so you want angle of pi/2 (=90 degrees) after 1/2 second.

or angle pi after 1 sec

That makes the equations x = 5cos(pi.t) and y = 5sin(pi.t)

Check: t=0 x = 5cos0 = 5 y = 5sin0 = 0
when t = 1/2 x = 5cos(pi/2) = 0 y = 5sin(pi/2) = 5
when t = 1 x = 5cos(pi) = -5 y = 5sin(pi) = 0
when t = 2 x = 5cos(2pi) = 5 etc etc y = 5sin(2pi) = 0

(c) Do a similar thing here for the parameter of the smaller wheel. But it's the x coordinate that has 10 added not the y coordinate.

See if that makes sense and works in the software. Post back if you want more help.

Bob

Math Is Fun Forum

#1 2014-03-03 14:09:49

Non-Linear Parametric motion help!!

#2 2014-03-03 16:07:48

Re: Non-Linear Parametric motion help!!

#3 2014-03-03 17:11:48

Re: Non-Linear Parametric motion help!!

#4 2014-03-03 20:15:30

Re: Non-Linear Parametric motion help!!

Board footer