There are many applications where you need to convert rotary, also known as circular, to linear motion or linear motion to rotational motion. In a car engine the linear motion of the pistons is converted to rotational motion at the flywheel. Rotational motion in your electric motor at times needs to be converted to linear motion to be useful in an application. The exercise that follows is one way you can envision how this conversion takes place.
Draw a circle approximately 10 inches in diameter on a piece of 5/8-inch plywood using a compass. Mark the centre of the circle with a pencil. Cut out the circle as accurately as possible with your jigsaw ( the circle does not have to be perfectly round). Drill a hole in the centre of the circle with a 1/4-inch drill bit. Drill another hole with the 1/4-inch bit approximately one inch in from the edge of the circle.
Cut a 1-inch-wide, 18-inch-long piece from your 5/8-inch plywood on your table saw. Cut holes with your 1/4-inch drill bit approximately one inch from each end of this piece
Cut a 12-inch-by-30-inch piece of your 5/8-inch plywood. Make a 24-inch-long, 3/8-inch-wide straight groove down the centre of the wood with a router, starting four inches from one end of the piece of plywood.
Bolt your 18-inch piece of wood to the hole near the edge of the circle with a 3/16-inch-nut and bolt, 3/4 inches long (with the nut on the top side). Screw the circle onto the centre of the large piece of plywood approximately six inches from the end so that the edge of the circle is overlapping the centre groove by about two inches. Use a 3/4-inch-long wood screw. Pass a screw through the groove in the large piece of plywood and loosely bolt the other end of the 1-inch piece so that it is not too tight.
Turn the circle of plywood with your hand and you will notice that the bolt on the end of the 18-inch piece moves linearly up and down the board.
If you want an interesting effect you can glue a matchbook car to the bolt on the end of the 18-inch piece and have the car go up and down the wood linearly.
Do not screw the circle into the wood too tightly as you will have difficulty turning it. The bolt through the groove should also be quite loose to allow free movement.