Exploration
A unit circle is a circle with a radius of 1, graphed on a Cartesian plane, with the center of the circle at the origin. The relationship between the angle of different radii on the circle and the values of different points on the circle can help in the understanding trigonometric functions.
Objective
Exploration
The moment of inertia (MOI) is the rotational inertia of an object as it rotates about a specific axis. Moment of inertia determines the torque required for a specific angular rotation about an axis. The moment of inertia depends upon the distribution of mass of the rotating object in relation to the axis the object is rotating about.
Objective
Exploration
The moment of inertia (MOI) is the rotational inertia of an object as it rotates about a specific axis. Moment of inertia determines the torque required for a specific angular rotation about an axis. The moment of inertia depends upon the distribution of mass of the rotating object in relation to the axis the object is rotating about. Explore whether the stability of a book’s rotation is dependent upon the moment of inertia and therefore whether it changes based on the axis the book is rotating about.
Objective
Exploration
An inertial force arises from the rotation of the object and the object mass (sometimes called the centrifugal force, not to be confused with centripetal force). If the inertial force is greater than the force of friction, the object will slide off of the rotating turntable (following Newton’s First Law of Motion). The parameters that cause the inertial force to be greater than the force of friction depend on many variables.
Objective
Exploration
An object experiencing a constant net force will experience a constant acceleration. Acceleration is defined as either a change in speed or a change in direction. When an object moves along a curved path it may maintain its speed, however it will be constantly changing its direction of movement. This type of acceleration along a curved path is called centripetal acceleration and is the result of a centripetal force, a force that is directed inward, toward the center of the curvature of the path. Examine the figure below.
Exploration
When two cans of different geometries are released from rest at the same time at the top of an inclined plane the results of the race may not be what you predict. The moment of inertia of each soup can will affect whether it reaches the end of the inclined plane first.
Objective
In this experiment, students will:
1. Determine the order in which each can will reach the bottom of the ramp first and explain why in terms of the energy in the system and the moment of inertia in each can.
