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Rotational motion

Table of contents

Angular momentum

Torque

Forces and Torques in Muscles and Joints

Coriolis effect, and the Foucault Pendulum

Why don’t we feel the rotation of the Earth?

Artificial gravity in a space station

Angular momentum and the formation of our Solar System

PowerPoint presentations

Honors Physics  Rotational Motion PPT Chap 12 Hewitt

AP Physics  Rotational Motion PPT presentation: Giancoli Physics

Radians

With circular motion we use radians instead of degrees.

The radian is a unit of plane angle

1 radian =  360/ degrees =  57.296 degrees.

A radian is the standard unit of angles in all areas of mathematics beyond the elementary level.

One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

It follows that the magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or 2πr /r, or 2π.

Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees.

Well outside the boundaries of this high-school course, one may eventually encounter the steradian , a three-dimensional analogue of the radian.

{Above text adapted from Wikipedia.}

Problem solving

Solving rotational motion problems is very similar to solving for linear motion problems.

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transrot_table
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Moment of inertia – definition (to be added)

Moment of inertia – examples (to be added)

Moment of inertia – How does this affect an object’s behavior?

On FunctionSpace, William James posted this:

This GIF nicely explains the behaviour of objects as they roll down the inclined plane.

All the bodies have the same radius.

The surface is assumed to have sufficient friction as to cause pure rotation.

I=k*mr2

The objects in the decreasing order of their moment of inertia-

  • Green-Ring k=1 comes fourth
  • Red-Hollow sphere k=2/3=0.66 comes third
  • Blue-Solid cylinder k=0.5 comes second
  • Orange-Solid sphere-k=2/5=0.4 comes first

The acceleration of each object is inversely dependent on ‘k’.

image from https://en.wikipedia.org/wiki/Moment_of_inertia#/media/File:Rolling_Racers_-_Moment_of_inertia.gif

Learning Standards

SAT Subject Test in Physics
Circular motion, such as uniform circular motion and centripetal force

2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion is a
mathematical model describing change in motion (the acceleration) of objects when
acted on by a net force.

HS-PS2-10(MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations

Massachusetts Science and Technology/Engineering Curriculum Framework (2006)
1. Motion and Forces. Central Concept: Newton’s laws of motion and gravitation describe and predict the motion of most objects.
1.8 Describe conceptually the forces involved in circular motion.

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