Rotational Motion

Introduction

Rotational motion takes many of the concepts discussed for linear motion and redefines them for objects moving in circular paths. We will start with rotational kinematics and define angular displacement, angular velocity, and angular acceleration. The kinematic equations will be rewritten for these definitions. For rotational dynamics, we will introduce moment of inertia, which is a function of mass, shape, and torque. Torque occurs when a force is applied away from the center of rotation of an object.

Essential Questions

What is the magnitude and direction of the torque associated with a force?
What is the torque on a rigid object due to gravity?
How can the relative rotational inertia of a set of symmetrcal objects of equal mass be determined?
How can we determine by what factor an object's rotational inertia changes if all its dimensions are increased by the same factor?
How can the rotational inertia of a collection of point masses lying in a plane about an axis perpendicular to a plane be determined?
How can the rotational inertia of a thin rod of uniform density, about an arbitrary axis perpendicular to the rod be determined?
How can the rotational inertia of a thin cylindrical shell about its axis, or an object that may be viewed as being made of coaxial shells be determined?
What is the parallel-axis theorem and how can it be applied?
What is the analogy between translational and rotational kinematics and how can it be applied?
How can the right-hand rule associate an angular velocity vector with a rotating object?
What is the analogy between fixed-axis rotation and straight line translation?
What is the angular acceleration with which a rigid object is accelerated when subjected to a external torque or force?
What is the radial and tangential acceleration of a point on a rigid object?
How can rotational dynamics be applied to strings and massive pulleys?
How can the relationship between linear and angular quantities for an object of circular cross-section that rolls without slipping along a fixed plane be applied?
How can the equations of translational and rotational motion be applied simultaneously to analyze rolling without slipping?

Key Terms

Angular displacement - The angle in radians that an object moves at it rotates.
Angular velocity - Rate of change of angular displacement.
Angular acceleration - Rate of change of angular velocity.
Torque - A measurement of the tendency of a force to cause rotation.
Moment of Inertia - Resistance to change in rotation.

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