A 4-centimeter rod is attached at one end A to a point on a wheel of radius 2 cm
ID: 2837703 • Letter: A
Question
A 4-centimeter rod is attached at one end A to a point on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 3.5 rev/sec. Thus, when t=1/21 sec, the rod is situated as in the diagram at the right below.
(a) How far is the right end of the rod (the point B) from the center of the wheel at time t=1/21 sec?
(b) Express the x-coordinate of the right end of the rod as a function of t:
(c) Express the speed of the right end of the rod as a function of t: .
Explanation / Answer
For B, if you think about only the x position of the circle, the end of the rod will always be 4 cm to the right of it. The x position of the circle is given by 2cos(7pi*t), so the end of the rod will always be 2cos(7pi*t) +4
For C, we need to realize that 2cos(7pi*t) +4 gives the position of the end of the rod. Therefore, to get the speed, we need to take the derivative w/ respect to time, and we get
-14pi * sin(7pi*t) = velocity