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Rotational motion, Angular displacement, angular velocity, angular acceleration Rotational energy Moment of Inert

Chapter 10:Rotation of a rigid object about a fixed axis Part 1. Reading assignment: Chapter 10.6-10.9 (know concept of moment of inertia, don’t worry about integral calculation) Homework : (due Wednesday, Oct. 12, 2005): Chapter 10: 32, 35, 48, 55, 80. Rotational motion,

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Rotational motion, Angular displacement, angular velocity, angular acceleration Rotational energy Moment of Inert

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  1. Chapter 10:Rotation of a rigid object about a fixed axis Part 1 Reading assignment: Chapter 10.6-10.9 (know concept of moment of inertia, don’t worry about integral calculation) Homework : (due Wednesday, Oct. 12, 2005): Chapter 10: 32, 35, 48, 55, 80 • Rotational motion, • Angular displacement, angular velocity, angular acceleration • Rotational energy • Moment of Inertia (Rotational inertia) • Torque • For every rotational quantity, there is a linear analog.

  2. Rotational motion Look at one point P: Arc length s: Thus, the ___________ ________ is: Planar, rigid object rotating about origin O. q is measured in degrees or radians (more common)

  3. s = r r One __________ is the angle subtended by an arc length equal to the ___________ of the arc. q For full circle: Radian degrees 2p 360° p 180° p/2 90° 1 57.3° Full circle has an angle of 2p radians, Thus, one radian is 360°/2p = _____

  4. Define quantities for circular motion (note analogies to linear motion!!) Angular ______________: _________ angular speed: ____________ angular speed: Average angular _____________: Instantaneous angular ______________:

  5. Angular quantities are vectors Angular velocity, angular acceleration, angular momentum, torque. Right-hand rule for determining the direction of this vector. Every ________ (of a ________ object): • rotates through the same angle, • has the same angular velocity, • has the same angular acceleration. q, w, a characterize rotational motion of entire object

  6. Linear motion with constant linear acceleration, a. Rotational motion with constant rotational acceleration, a.

  7. Black board example 11.1 A wheel starts from rest and rotates with constant angular acceleration and reaches an angular speed of 12.0 rad/s in 3.00 s. • What is the magnitude of the angular acceleration of the wheel? • Through what angle does the wheel rotate in these 3.00 s? • Through which angle does the wheel rotate between t = 2.00 s and 3.00 s?

  8. Relation between linear and angular quantities Caution: Measure angular quantities in radians Arc length s: Tangential speed of a point P: Tangential acceleration of a point P: Note, this is not the centripetal acceleration ar !!

  9. Black board example 11.2 • The diameters of the main rotor and the tail rotor of a helicopter are 7.60 m and 1.02 m, respectively. The respective rotational speeds are 450 rev/min and 4138 rev/min. • Calculate the speeds of the tips of both rotors. • Compare with the speed of sound, 343 m/s. • The rotors are rotating at constant angular speed. What is the centripetal acceleration and what is the angular acceleration?

  10. Black board example 11.3 HW 27 • What is the angular speed w about the polar axis of a point on Earth’s surface at a latitude of 40°N • What is the linear speed v of that point? • What are w and v for a point on the equator? Radius of earth: 6370 km

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