A twelve foot long rod is attached at one end A to a point o

A twelve foot long rod is attached at one end A to a point on a wheel of radius 4 feet, centered at the origin. The other end B is free to move back and forth along the x-axis. The point A is at (4, 0) at time t = 0, and the wheel rotates counterclockwise at 3 rev/sec.

8 12 16 time t = 0 8 12 16 time t >0 4

Solution

The movement of point A can be described as a cosine function

frequency = 3 rev/sec

radius = 4 feet

So, x = 4 cos(2pi*3t) = 4cos(6pi*t)

y = 4sin(6pi*t)

The movement of point B is described as : y =0

x = length of rod + 4cos(6pi*t) = 12 +4cos(6pi*t)

At t=1 : Point A : x = 4cos6pi = 4

y = 4sin6pi =0

( 4 , 0 )

At t= 1: Point B x = 12 +4cos6pi = 16

(16 , 0)