2008 AAPT Summer Meeting
Showing the Tangent Trajectory of a Ball coming from Circular Motion when the Centripetal Force on the Ball is Suddenly Reduced to Zero- using a water sensitive mat
Wayne D. Peterson
Brigham Young University
Physics and Astronomy Department
Provo, Utah 84602
801 422 3144
An “Aquadoodle Tangent Trajectory Apparatus” is made using a water sensitive mat (called “aquadoodle”) made by Spin Master Ltd. A wet ball makes a circular path when circulating around the inside of a cylinder placed on the mat. If the cylinder is removed, the ball leaves a straight line path that is tangent to the circular path. This demonstration can be used as an example of how Newton’s laws apply to circular motion.
Construction of Apparatus:
Start with an 18 inch turntable which is commonly called a “lazy Susan”, a six inch plastic cylinder, a Spin Master “aquadoodle” mat, and a “squash” ball from a sporting- goods store. Peel the cover off of the top of the turntable. Using a screwdriver, pry loose the fastener that sticks up through the center of the turntable. Remove the ball bearing ring and housing from underneath the turntable. Remove the glue that was left from peeling off the top cover (the glue should come off by pushing the glue into a ball of glue with your thumb or fingers). The top of the turntable has a raised rim on its perimeter. The top of the turntable has a groove which separates the top surface into an outer ring and a central island. The central circular island will be covered with “aquadoodle” mat. Cut out a circular section of “aquadoodle” mat that is a little bit larger than the central island.
1 sided glue method:
Mask the turntable so that only the central island is showing. Coat the central island with a layer of Spray Glue. With the “write on side” up, fold the “aquadoodle” mat slightly so that the middle of the “aquadoodle” mat can be put down on the center of the island first. Flatten the “aquadoodle” mat by pressing it down from the center to the outside. Trim the excess mat with a razor blade so that the mat covers the top of the island exactly.
2 sided glue method:
The procedure is the same as the one sided method except the back side of the mat gets sprayed also.
The cylinder used for this demonstration needs to be heavy so that it will stay in place when its platform gets tipped back and forth. A PVC Bushing was chosen, but another type cylinder might work just as well. The bottom end of the PVC Bushing is the end without an inner rim. Sand the bottom end of the cylinder with #60 grit sand paper. This roughens the bottom surface of the cylinder. The rough surface provides enough contact friction between the cylinder and the mat to keep it in place when tipped back and forth. A plastic jar filled with water is used to wet the surface of the squash ball.
Use of Apparatus:
Suppose a ball is in uniform circular motion. If the centripetal force is suddenly reduced to zero, what will be the motion of the ball? Some students might think it will exit the circle in a radial direction. Others might think it will spiral away from the center of the circle.
For an object in uniform circular motion, the velocity vector is always tangent to the circular path of the object. The direction of the velocity changes so there is a force on the object called centripetal force. The centripetal force is the only force acting upon the object. This force only changes the direction of the velocity of the object. Assuming no friction, no force is needed to keep the object moving. Therefore if the centripetal force suddenly becomes zero, the direction of the velocity does not change any more. The object then moves in the direction that the velocity vector was pointing when the centripetal force became zero. Its path is straight and is tangent to the circular path.
Place the cylinder on the center of the “aquadoodle” mat. Wet the entire surface of the squash ball. A squash ball is used because it is somewhat hydrophilic. Place the ball on the inside of the cylinder against the inside wall. Pick up the turntable. Tip it and move it in a circular type motion to get the ball moving around the inside of the cylinder. Keep the velocity of the ball low so that it does not ride up on the cylinder wall. Set the turntable down on a flat surface. Lift the cylinder straight up off of the surface, releasing the ball. The ball will trace a path that is tangent to the circular path. The groove in the turntable helps to keep the ball from coming back across the mat after it bumps the rim of the turntable. To do the demonstration again, the warm air from a small hair dryer could be used to erase the path of the ball.
“Tangent Path” shown using the “Aquadoodle Tangent Trajectory Apparatus”
Equipment and costs required to construct the apparatus:
Item Source Part Number Cost
____ ______ __________ ____
18 inch turntable Bed Bath and Beyond Copco 14.99
(lazy Susan) (Orem, Utah) Non-Skid Turntable
Wilton Industries, Inc
PVC cylinder Sprinkler World 6 inch IPSxPIP 9.21
(Harward Irrigation Bushing 431-060 ¼
Aquadoodle Wall Toys R Us Spin Master 14.98
Mat (Orem, Utah)
Squash Ball Sports Authority Prince Sports Inc 2.99
Plastic Jar Maceys (Grocery Store Western Family Round 2.49
Provo, Utah Servables 2 Cup
Spray Adhesive Lowes Dap All-Purpose 7.02 (Orem, Utah) Spray Glue
Sand Paper Lowes 3M Aluminum Oxide 2.27
(Orem, Utah) #60 grit 9x11 5 pack
Razor Blades Lowe’s single edge 10 pack 1.98
(Orem, Utah) item # 79621