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# Rotational Motion: Spinning Objects

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Author: Janice VanCleave

A rotating object spins about an axis, which is an imaginary line through the center of the object. This axis can be real, such as the axle of a wheel on a vehicle, or imaginary, such as that through a rolling ball or hoop. If an object is rolling down an incline or across a level plane, it is spinning about the axis as the axis is being translated (moved from one location to another). Mechanical energy is the energy of an object that is moving or has the potential of moving. For rotating objects, part of the mechanical energy is due to rotational energy.

In this project, you will compare the mechanical energy of rotating objects of different shapes—including different-size spheres, a hollow and a solid sphere, a cylinder, and hoops—on an incline and on a level surface.

### Getting Started

Purpose To determine the effect of size on mechanical energy of two rotating spheres on an inclined plane.

### Materials

• 2 or 3 books 12-by-36-inch (30-cm-by-90-cm)
• stiff cardboard (Size is not critical; a board of comparable size can be used.)
• bath towel
• marker
• ruler
• 2 glass marbles of different radii

### Procedure

1. Stack the books on the floor and make a ramp (an inclined plane) by supporting one short end of the cardboard on the pile of books.
2. Stretch the towel on the floor at the end of the cardboard ramp. This will help stop the spheres when they leave the ramp.
3. Use the marker to draw a line across the ramp about 4 inches (10 cm) from the top edge. Hold the edge of the ruler on this line, and place the marbles behind the ruler.
4. Lift the ruler to allow the marbles to roll down the ramp. Observe the marbles and determine which one reaches the end of the ramp first.

### Results

The marbles reach the end of the ramp at the same time.

### Why?

Energy is the capacity to move something. In other words it is the ability to do work. Potential energy (PE) is the stored energy of an object due to its position or condition. Objects have potential energy when work is done on them, such as lifting an object or compressing a spring. Objects with potential energy have the potential to do work. In reference to an arbitrary position where the potential energy of an object is defined as zero, if the object is raised above this position it is said to have gravitational potential energy. Kinetic energy (KE) is the energy possessed by an object resulting from the motion of that object. Another way of describing the kinetic energy of an object is to consider how it moves. Kinetic energy of an object with translational motion (motion in which the center of mass of an object moves from one place to another) is translational kinetic energy. Rotation is the turning motion of objects about their axis, and the kinetic energy due to rotation is called rotational kinetic energy.

Mechanical energy (Em) is the energy of motion. It is the energy of an object that is moving or has the potential of moving. Total mechanical energy is the sum of the potential and kinetic energies of an object; thus, Em = KE ÷ PE. At the top of the ramp, both marbles have the same total mechanical energy. In a perfect condition in which there would be no loss of energy due to air resistance or any other frictional force acting on the marbles, the mechanical energy of the marbles would be conserved. This means that the maximum mechanical energy of each marble at the top of the ramp is equal to its maximum mechanical energy at the bottom of the ramp. At the top of the ramp, the KE of the marbles equals zero, so they have only gravitational potential energy, GPE. As they move down the ramp, their height decreases and their rotational speed (the speed of an object rotating about its axis) and translational speed (the speed of an object being moved from one place to another) increase; thus their KE increases and their PE decreases until at the bottom, ground zero, the PE equals zero. This relationship between PE and KE is called the law of conservation of mechanical energy. The fact that the glass marbles have different sizes yet reached the bottom of the ramp at the same time indicates that their size did not affect their mechanical energy.

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