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Which Objects Store More Rotational Energy Using an Inclined Plane?

Physics is the science that deals with physical objects. It has been studied since the days of Sir Isaac Newton, who developed equations for gravity. Objects that roll down a hill, also called an inclined plane, also have unique energy properties. Physicists have studied the properties of rolling objects, and developed equations that lead to the understanding of the energy used and stored.

Interpreting a Physics Law
- One of the chief equations of physics is that force is equal to mass times acceleration. This is written as F = M x A. Sir Isaac Newton wrote about it, but debate is continuing whether he actually developed it. Consider all the variables and fixed attributes of a rolling object down a hill, technically called an inclined plane. The acceleration (A) is imparted by gravity, so you can't change that. The only thing you can change is the object's mass. On Earth, mass and weight are the same.
Different Weights
- Since F = M x A, the heavier the weight, the more force will occur at the bottom of the plane when the object stops. Suppose you have two spheres, one weighs 2 pounds and the other one weighs 10 pounds. Gravity, the "A," is 32 feet per second squared. For the sake of simplicity, presume you roll the object for exactly one second on an inclined plane one foot off the ground. Solving the equation for a 2-pound sphere, the end result is 64 foot pounds of energy. For a 10-pound sphere, the result is 320 foot pounds of energy. All this is presuming you are using the same inclined plane. Notice that even though the weight difference is only 8 pounds, the force difference is 256 foot pounds.
Moments of Inertia
- The moment of inertia is how much energy is stored in an object. For a sphere, the equation is 2/5 x M x R squared, with M being the mass and R being the radius. Suppose you have two spheres, with a radius of 1 foot. One weighs 2 pounds and one weighs 10 pounds. Solving the equation, the moment of inertia at the bottom of the inclined plane would be 0.8 pounds for a 2-pound sphere. The moment of inertia for a 10-pound sphere would be 4 pounds.
End Result
- All the aforementioned equations all point to the same thing: The heavier an object, the more force it exerts at the bottom of the plane. Think of it this way: You have a ball of lead and a ball of Styrofoam, both with the same diameters, at the top of the plane. You place a thin wood block at the bottom. You release both balls at the same time. The lead ball will break through the wood, but the Styrofoam ball will be stopped by the wood.

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