1 / 6

PHY221 Ch15: // Axis Theorem and Torque

PHY221 Ch15: // Axis Theorem and Torque. Recall main points: Expression of the Kinetic energy of a rigid body in terms of Kcm and Icm Parallel Axis Theorem Torque and Cross Product Angular acceleration from the torque. PHY221 Ch15: // Axis Theorem and Torque. Main Points.

tejano
Download Presentation

PHY221 Ch15: // Axis Theorem and Torque

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. PHY221 Ch15: // Axis Theorem and Torque • Recall main points: • Expression of the Kinetic energy of a rigid body in terms of Kcm and Icm • Parallel Axis Theorem • Torque and Cross Product • Angular acceleration from the torque

  2. PHY221 Ch15: // Axis Theorem and Torque Main Points • Kinetic energy of a rigid body in terms of Kcm and Icm In the 3rd slide of Ch 13 we showed that the total kinetic energy of a system is equal to the energy of the Center of Mass (CM) plus the energy RELATIVE to the CM: CM  vCM In our case since we study RIGID bodies, any motion relative to the CM MUST be a rotation around an axis through the CM. And therefore, since : This is a general result that should be used when the work-energy theorem, or the conservation of mech. energy, is used for solving problems involving rigid bodies rotating . Note that any motion can be viewed as the CM motion PLUS a rotation AROUND an axis thru the CM

  3. PHY221 Ch15: // Axis Theorem and Torque Main Points • Optional: Direct proof of the preceding result: By definition of the center of mass (see CM chapter) the last term is zero. Note also that we replaced vi/cmby ri/cm since we are dealing with a rigid body. We obtain the fundamental result:

  4. PHY221 Ch15: // Axis Theorem and Torque Main Points • Parallel Axis Theoremvia K=Kcm+1/2Iw2 Using the result on the previous slides, we can arrive at the very useful parallel axis theorem:

  5. PHY221 Ch15: // Axis Theorem and Torque Main Points • Torque and Cross product: The torque is defined as: Right Hand Rule: In this course we only look at rotations around a axis of fixed direction, therefore, . In the problems you are given, the forces are always in the X-Y plane and the r should always be the vector r=(x,y) and thus  is the angle in the x-y plane. The magnitude of the torque around the z-axis is: F  m y r x O

  6. PHY221 Ch15: // Axis Theorem and Torque Main Points Angular acceleration from the torque, using Newton’s 2nd law:

More Related