Key concepts
Physics
Gravity
Friction
Centripetal force
Normal force
Rotational motion
Newton's laws of motion

Introduction
Are you any good at hula-hooping? If not, don’t worry—you can do this fun project without any hula-hooping experience. You will examine some of the fascinating physics behind hula-hooping using just a pencil and a rubber band.

Background
Hula-hooping is all about forces! You might not think about physics much when you play with a Hula-Hoop, but there are many different forces at work that help keep a Hula-Hoop spinning and prevent it from falling to the ground. A force is a push or a pull that acts on an object. Forces can make things move, but just because something isn’t moving doesn’t mean it doesn’t have any forces acting on it. For example, if you're sitting in a chair right now, the chair is exerting an upward force on you that prevents you from falling to the ground. Conversely, just because something is moving doesn’t necessarily mean it has force acting on it. An object moving at a constant velocity will keep moving in a straight line forever if there are no forces to slow it down (Newton's first law of motion).

So what forces act on a Hula-Hoop?

—Weight, or the force of gravity pulling the Hula-Hoop down;

—Friction, the force that opposes motion between two surfaces that are sliding against each other (so in this case, the friction between the Hula-Hoop and your clothes);

—The normal force. In physics, “normal” means “perpendicular to” not “regular” as it does in everyday speech. The normal force is that which acts perpendicular (at a right angle) to two surfaces that touch each other. For example, a book sitting on a table has a normal force from the table pushing it up, which prevents it from falling. If you push your hand against a wall, the wall exerts a horizontal normal force against your hand (Newton's third law of motion);

—The centripetal force, which is the force that keeps a rotating object moving in a circle, instead of flying off in a straight line. Imagine, for example, twirling a rock on a string. The tension in the string pulls on the rock and makes it move in a circle. If you suddenly cut the string, there is no more centripetal force acting on the rock and it will fly away instead of continuing to move in a circle. In a Hula-Hoop the centripetal force results from your body pushing on the hoop (a combination of the frictional and normal forces).

As you will see, the combined effect of all these forces determines the Hula-Hoop's motion (Newton's second law of motion).

Materials

• Pencil
• Rubber band

Preparation

• Hold the pencil by the eraser end and point the tip up.
• Loop the rubber band over the pencil, so it falls down to your fingers.

Procedure

• Slowly start twirling the pencil. What happens?
• Keep twirling the pencil faster and faster. How fast do you have to twirl it before the rubber band starts moving up?
• Stop twirling. What happens?
• Try to twirl the pencil so fast that you get the rubber band to fly off the tip. Can you get it to work?
• Try changing the angle of the pencil as your twirl it. Meaning, you do not keep the pencil perfectly vertical as you twirl it. You can pinch the eraser end with your fingers and spin the tip around in a circle, tracing out a three-dimensional cone. What happens if you make this “cone” wider? Does it make it easier or harder to make the rubber band move upward?
• Try rotating your wrist as you twirl the pencil, so the pencil becomes horizontal and eventually upside down (so the tip points downward). Can you keep the rubber band on the pencil even when it's upside down?
• Extra: Try using different size rubber bands. What’s easier to twirl, a big or a small one?

Observations and results
In this activity the pencil acts like a person’s body and the rubber band acts like a Hula-Hoop. And just like with a real Hula-Hoop, you should have found that if you did not spin the pencil fast enough, the rubber band would fall down. As you spin the pencil faster and/or make the cone you trace with the pencil wider, the rubber band should start to move up the pencil and eventually fly off the tip!

To understand this, you can refer back to the information in the background section. Remember the example about centripetal force and twirling a stone on a string? The stone “wants” to keep moving in a straight line but the centripetal force from the string makes it move in a circle. The rubber band behaves in a similar manner. It “wants” to fly off in a straight line but the centripetal force from the pencil makes it move in a circle. If you spin the pencil fast enough, the centripetal force is no longer strong enough to hold the rubber band in place—so it starts sliding outward (and upward). This makes it very difficult, if not impossible, to keep the rubber band on the pencil when you hold it upside down.

More to explore
Swiveling Science: Applying Physics to Hula-Hooping, from Scientific American
Newton's Laws of Motion, from NASA
Inclined Planes, from the Physics Classroom
Science Activities for All Ages!, from Science Buddies

This activity brought to you in partnership with Science Buddies