Parallel Axis Theorem - Physics for Scientists and Engineers I - Lecture Slides, Slides of Engineering Physics

Download Parallel Axis Theorem - Physics for Scientists and Engineers I - Lecture Slides and more Slides Engineering Physics in PDF only on Docsity!

Today’s Concepts:

a) Parallel Axis Theorem

b) Torque & Angular Acceleration

Parallel Axis Theorem

A ball of mass 3 M at x  0 is connected to a ball of mass M at x  L by a massless rod. Consider the three rotation axes A , B , and C as shown, all parallel to the y axis.

For which rotation axis is the moment of inertia of the object smallest? (It may help you to figure out where the center of mass of the object is.)

B

3 M M

A C

0 L /4 L /

x

y

L

CheckPoint

Right Hand Rule for finding Directions

Why do the angular velocity and acceleration point perpendicular to the plane of rotation?

ACT

A ball rolls across the floor, and then starts up a ramp as

shown below. In what direction does the angular

acceleration vector point when the ball is rolling up the ramp?

A) Into the page

B) Out of the page

Torque

 = rF sin(  )

Similarity to 1D motion

ACT

Strings are wrapped around the circumference of two solid

disks and pulled with identical forces. Disk 1 has a bigger

radius, but both have the same moment of inertia.

Which disk has the biggest angular acceleration?

A) Disk 1

B) Disk 2

C) same F F

w 1 w 2