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Unformatted text preview: 1 Chapter 10 Rotation Angular displacement (symbol: ) Average and instantaneous angular velocity (symbol: ) Average and instantaneous angular acceleration (symbol: ) Rotational inertia also known as moment of inertia (symbol I ) Torque (symbol ) Rotational Kinetic Energy 2 In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. An object can move AND rotate. 3 The Rotational Variables A rigid body is defined as one that can rotate with all its parts locked together and without any change of its shape. A fixed axis means that the object rotates about an axis that does not move. We can describe the motion of a rigid body rotating about a fixed axis by specifying just one parameter. Consider the rigid body of the figure. 4 Take the the z-axis to be the fixed axis of rotation and define a reference line which is fixed in the rigid body and is perpendicular to the rotational axis. The figure above shows a top view. The angular position of the reference line at any time t is defined by the angle (t) that the reference lines makes with the position at t = 0. The angle (t) also defines the position of all the points on the rigid body. The angle is related to the arc length s traveled by a point at a distance r from the axis via the equation: s r = Note: The angle is measured in radians . 5 Conceptual Example A Total Eclipse of the Sun The diameter of the sun is about 400 times greater than that of the moon. By coincidence, the sun is also about 400 times farther from the earth than is the moon. For an observer on the earth, compare the angle subtended by the moon to the angle subtended by the sun and explain why this result leads to a total solar eclipse. 400 400 400 400 sun moon sun moon sun moon moon sun moon sun moon moon s s r r s s s r r r = = = = = = r s = = Radius length Arc radians) (in 6 t 1 t 2 1 2 1 2 2 1 The picture shows the reference line at a time and at a later time . Between and the body undergoes an angular displacement . All the points of the rigid bod Angular Displacement t t t t = y have the same angular displacement because they rotate locked together. 7 ( ) 1 2 1 2 1 2 Average angular velocity for the time interval , is defined as the ratio: The instantaneous angular velocit Angular Velocity radians/seco The SI unit for angular velocity is nd avg t t t t t = = y is defined as the limit of as lim t t t t = t 1 t 2 d dt = 8 1 2 t 1 t...
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This note was uploaded on 10/18/2011 for the course PHYS 101 taught by Professor Cohen during the Spring '10 term at Pittsburg State Uiversity.
- Spring '10