Using sine equation to solve word problem

Question

A bicycle tire has a diameter of 24 inches and is revolving at a rate of 10rpm. At t=0, a certain point is at a height of 0. What is the height of the point above ground after 3 seconds?

Answer 1

Hi Ann:

 

first let's try to use our common sense.  A rate of 10 rpm (rotation per minute) means that 60 s / 10 rotations = 6 seconds per rotation.  It takes the wheel 6 seconds to complete a full rotation.  Therefore, half a rotation will be done in half the time, 3 s.  So the bottom point in contact with the ground at time zero, will move half a rotation, which means to the opposit side of the diameter across the center; now its height is equal to the diameter of the wheel, 24 inches.  Always easier to draw on paper.

 

Or you can draw a circle, with its center at the origin, and the angle reference axis (x) vertical downward, going through point A in contact with the ground.  As the wheel moves, the angle of point A increases towards the right; the angle is given by:

 

theta = omega * time = 10 rpm * 360 degrees / rotation * 1 minute / 60 s = 60 * time [degrees]

 

At time t = 3 s, the angle is now 180 degrees, point on the very top of the wheel, at maximum height of diameter.

 

Hope this helps.

 

  Jean-Michel