Rotational Mechanics

Syllabus, Handouts and PowerPoint lectures for this unit: Calendar | Handouts | Lectures

Click on these links for the assessments below for videos and examples ; -)

Group Quizzes: 8.2 .:. 8.3

Lab for this unit:  Gyroscope Investigation .:. Ezekiel's Wheel .:. Angular Momentum 

Assessments: 8.1 - Rotational Kinematics .:. 8.2 - Rotational Dynamics .:. 8.3 - Rotational Energy and Momentum

8A.    Understand basic angular quantities like angle, angular velocity and angular acceleration.

8B.    Understand how to do conversions involving radians, rotations, radians per second, RPM, and rotations per second.

8C.    Understand how to use tangential relationships with angle, angular velocity, and acceleration.

Distance and angle:

Tangential Relationships #1 (find s)

Tangential Relationships #2 (find angle)


Velocity and angular velocity (omega):

Tangential Relationships #3 (find v)

Tangential Relationships #4  (find omega)


Acceleration and angular acceleration (alpha):

Tangential Relationships #5 (find a)

Tangential Relationships #6 (find alpha)


Tangential with unit conversions:

Tangential Relationships #7 (rot, r to find s)

Tangential Relationships #8 (s, r to find rot)

Tangential Relationships #9 (RPM, r to find v)

Tangential Relationships #10 (v, r to find RPM)

8D.    Use angular velocity to calculate centripetal acceleration.

Noteguide08D-CentripetalAcceleration.docx

Using Angular Velocity to Calculate Centripetal Acceleration:

8E.     Solve problems with angular kinematics

(This is what we did the first day of the unit - If you missed the first day, go through these videos and the example problems and you should be fine.)

8F.    Calculate torque.

Noteguide08F-Torque.docx

Dynamics and Torque:

8G.    Calculate moments of inertia.

Noteguide08G-MomentOfInertia.docx

Calculating Moment of Inertia (rotational "mass")

8H.    Solve problems using F=ma

Noteguide08H-AngularDynamics.docx

Solving Angular Dynamics Problems:

8I.    Solve dynamics problems for an object rolling down an inclined plane.

Noteguide08I-Rolling Dynamics.docx

Solving Rolling Problems with Dynamics:

8J.    Solve complex dynamics problems that require systems of linear equations

Noteguide08J-ComplexDynamics.docx

Solving Complex Dynamics Problems:

8K.    Calculate rotational kinetic energy

8L.    Solve rolling problems using conservation of energy

Noteguide08L-RollingCOE.docx

Solving Rolling problems with Conservation of Energy:

Try this one:

Rolling COE Example

8M.    Solve complex problems using conservation of energy

Noteguide08M-ComplexCOE.docx

Solving Complex problems with Conservation of Energy:

The same problem solved with dynamics:

Complex Ex #1 Dynamics

More examples solved with Dynamics and Energy:  (Look at the Energy ones for this flip)

(In my opinion it is easier to use energy)

Dynamics                                Energy

Ex #2 Dynamics                      Ex #2 Energy

Ex #3 Dynamics                      Ex #3 Energy

Ex #4 Dynamics                      Ex #4 Energy

Ex #5 Dynamics                      Ex #5 Energy

8N.     Calculate angular momentum

8O.    Solve problems with torque, time, moment of inertia and change in angular velocity

Noteguide08NOP-AngularMomentum.docx

Torque, Time, Moment of Inertia, and Angular Velocity:

8P.    Solve conservation of angular momentum problems.

Noteguide08NOP-AngularMomentum.docx

Conservation of Angular Momentum:

Sometimes Gyroscopic stability is cited as the reason bikes are stable.  There is more to it than that.....

8Q1.    Understand what the vector cross product is, and how to find the direction of it

The Definition of the Cross Product

Watch first

Examples of Cross Product Directions

Watch Second

8Q2.    Understand precession in terms of the vector nature of angular velocity and torque.

Gyroscopic Precession:

8R.    Understand the basic idea behind the Coriolis effect.

There is no noteguide - Just watch these two videos!!  : - )

The Coriolis Effect:

MIT:  (Watch this one too)