1 / 18

Rotational motion, Angular displacement, angular velocity, angular acceleration

Chapter 10:Rotation of a rigid object about a fixed axis Part 2. Reading assignment: Chapter 11.1-11.3 Homework : (due Wednesday, Oct. 12, 2005): Problems: Q4, 2, 5, 18, 21, 23, 24,. Rotational motion, Angular displacement, angular velocity, angular acceleration Rotational energy

gmessner
Download Presentation

Rotational motion, Angular displacement, angular velocity, angular acceleration

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 10:Rotation of a rigid object about a fixed axis Part 2 Reading assignment: Chapter 11.1-11.3 Homework : (due Wednesday, Oct. 12, 2005): Problems: Q4, 2, 5, 18, 21, 23, 24, • 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. 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

  3. Rotational energy A rotating object (collection of i points with mass mi) has a rotational ___________ energy of Where: Rotational inertia

  4. Demo: Both sticks have the same weight. Why is it so much more difficult to rotate the blue stick?

  5. Black board example 11.4 2 What is the rotational inertia? 3 1 4 • Four small spheres are mounted on the corners of a frame as shown. • What is the rotational energy of the system if it is rotated about the z-axis (out of page) with an angular velocity of 5 rad/s • What is the rotational energy if the system is rotated about the y-axis? • (M = 5 kg; m = 2 kg; a = 1.5 m; b = 1 m).

  6. Rotational inertia of an object depends on: • the ________ about which the object is rotated. • the __________ of the object. • the __________ between the mass(es) and the axis of rotation.

  7. Calculation of Rotational inertia for ____________ ________________ objects Refer to Table11-2 Note that the moments of inertia are different for different ________ of rotation (even for the same object)

  8. Rotational inertia for some objects Page 227

  9. Parallel axis theorem  Rotational inertia for a rotation about an axis that is ____________ to an axis through the center of mass h Blackboard example 11.4 What is the rotational energy of a sphere (mass m = 1 kg, radius R = 1m) that is rotating about an axis 0.5 away from the center with w = 2 rad/sec?

  10. Conservation of energy (including rotational energy): Again: If there are no ___________________ forces: Energy is conserved. Rotational _____________ energy must be included in energy considerations!

  11. Black board example 11.5 Connected cylinders. • Two masses m1 (5 kg) and m2 (10 kg) are hanging from a pulley of mass M (3 kg) and radius R (0.1 m), as shown. There is no slip between the rope and the pulleys. • What will happen when the masses are released? • Find the velocity of the masses after they have fallen a distance of 0.5 m. • What is the angular velocity of the pulley at that moment?

  12. Torque f A force F is acting at an angle f on a lever that is rotating around a pivot point. r is the ______________ between F and the pivot point. This __________________ pair results in a torque t on the lever

  13. Black board example 11.6 Two mechanics are trying to open a rusty screw on a ship with a big ol’ wrench. One pulls at the end of the wrench (r = 1 m) with a force F = 500 N at an angle F1 = 80 °; the other pulls at the middle of wrench with the same force and at an angle F2 = 90 °. What is the net torque the two mechanics are applying to the screw?

  14. Torque t and angular acceleration a. Newton’s __________ law for rotation. Particle of mass m rotating in a circle with radius r. force Fr to keep particle on circular path. force Ft accelerates particle along tangent. Torque acting on particle is ________________ to angular acceleration a:

  15. Definition of work: Work in linear motion: Component of force F along displacement s. Angle g between F and s. Work in rotational motion: Torque t and angular displacement q.

  16. Work and Energy in rotational motion Remember work-kinetic energy theorem for linear motion: External work done on an object changes its __________ energy There is an equivalent work-rotational kinetic energy theorem: External, rotational work done on an object changes its _______________energy

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

  18. Summary: Angular and linear quantities Linear motion Rotational motion Kinetic Energy: Kinetic Energy: Force: Torque: Momentum: Angular Momentum: Work: Work:

More Related