RKE - Introduction to Rotational Kinematics and Energy

Rotational Kinematics and Energy Overview

Introduction

With the possible exception of Uniform Circular Motion (UCM), one of the fundamental assumptions so far has been that models of objects in motion include only translation (linear motion) and rotation is not allowed. This led to the concept of a free body diagram in which all mass was assumed to be at an infinitesimal point at the center of mass. Even in the case of UCM, objects traveling in a circle are not allowed to spin. While this serves as a good model for a very large class of problems, it is inadequate to model an equally important class of problems that include rotation and rolling. Translational kinematics is fine for modeling the person on bicycle, but falls short of modeling why the person remains upright and making predictions using conservation of energy; for that we need to include rotational concepts. There are countless problems in everyday life that require the extension of physics to include rotation, from the tires on a car, a bowling ball careening toward the pins, the spin cycle of a washing machine to the spinning of a DVD, just to name an extremely few examples.

Essential Questions

1. What are the angular kinematic quantities?
2. How are the angular kinematic quantities related to the translational kinematic quantities?
3. What is the key difference between Uniform Circular Motion and Rotational Kinematics?
4. Is rotational kinetic energy conserved?
5. What is the rotational analog of mass?
6. What units are used to discuss angular kinematic quantities?
7. What is the difference between rotation and rolling?

Key Terms

1. angular acceleration - is the rate of change of angular velocity with respect to time (Greek letter alpha, )
2. angular displacement - the change in angle (Greek letter theta ) through which a physical or geometric object has been rotated in a specified sense about a specified axis, although not a vector, it is usually treated as a vector.
3. angular position - the angle relative to a specified polar origin of a rotated physical or geometric object.
4. angular velocity - the rate of change of angular displacement with respect to time (Greek letter omega, ). axis of rotation – the axis perpendicular to a rotating plane through the center of a circle traced by any point in the rotating plane.
5. centripetal acceleration - the acceleration vector, perpendicular to velocity and tangential acceleration, that makes a body follow a curved path. It is directed toward the center of curvature of the path.
6. moment - perpendicular distance from a point to a line, usually used to describe rotational quantities with the axis of rotation through the point and a physical quantity at the line in rotation about the given point.
7. moment of inertia - property of an object that resists changes in angular velocity, specified by both incremental mass and distance from an axis of rotation.
8. rolling - a type of motion that combines rotation of an object with translation of that object.
9. rotation - a circular movement of an object around an axis of rotation.
10. rotational kinetic energy - the rotational analog of kinetic energy, equal to one half the moment of inertia times the angular velocity squared.
11. rotational work - work done by a torque applied through an angle, equal to the change in rotational kinetic energy.
12. tangential acceleration - the acceleration vector, perpendicular to centripetal acceleration, that makes a body increase in angular velocity. It is directed tangent to the circle traced by a point rotating about an axis of rotation.

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