1 / 11

Understanding Torque and Centers of Mass in Physics

Learn about torque as the tendency to rotate, and how to calculate centers of mass for various shapes. Discover the importance of balance and gravitational forces in physics.

middlebrooks
Download Presentation

Understanding Torque and Centers of Mass in Physics

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. Photo by Vickie Kelly, 1998 Greg Kelly, Hanford High School, Richland, Washington Chapter 7 Extra Topics Crater Lake, Oregon

  2. Torque is a function of force and distance. (Torque is the tendency of a system to rotate about a point.) Centers of Mass: Lake Superior, Washburn, WI Photo by Vickie Kelly, 2004

  3. If the forces are all gravitational, then If the net torque is zero, then the system will balance. Since gravity is the same throughout the system, we could factor g out of the equation. This is called the moment about the origin.

  4. If we divide Moby the total mass, we can find the center of mass (balance point.)

  5. For a thin rod or strip: d = density per unit length (d is the Greek letter delta.) moment about origin: mass: center of mass: For a rod of uniform density and thickness, the center of mass is in the middle.

  6. strip of massdm distance from the y axis to the center of the strip distance from the x axis to the center of the strip Moment about x-axis: Center of mass: Moment about y-axis: Mass: For a two dimensional shape, we need two distances to locate the center of mass. y x x tilde (pronounced ecks tilda)

  7. For a plate of uniform thickness and density, the density drops out of the equation when finding the center of mass. For a two dimensional shape, we need two distances to locate the center of mass. y x Vocabulary: center of mass = center of gravity = centroid constant density d = homogeneous = uniform

  8. coordinate of centroid = (2.25, 2.7)

  9. square rectangle circle right triangle Note: The centroid does not have to be on the object. If the center of mass is obvious, use a shortcut:

  10. When a two dimensional shape is rotated about an axis: Theorems of Pappus: Volume = area . distance traveled by the centroid. Surface Area = perimeter . distance traveled by the centroid of the arc. Consider an 8 cm diameter donut with a 3 cm diameter cross section: 1.5 2.5

  11. We can find the centroid of a semi-circular surface by using the Theorems of Pappus and working back to get the centroid. p

More Related