1. Rotational Vectors and Angular Momentum

2. Angular Velocity
Angular velocity is a vector and its direction is perpendicular to the plane of rotation.
Right-hand Rule: Curl your fingers in the direction of rotation, then the thumb points in the direction of angular velocity.
Counter-clockwise rotation - Positive
Clockwise rotation - Negative

3. Angular Acceleration
What is the average angular acceleration for a top when the angular velocity goes from to in 0.5s?

4. Torque Magnitude - Direction - Use the right hand rule.
Mathematically -
Matrix Method - Find the determinant of the following matrix.

5. Torque Example
What is the torque exerted about the origin by a force if it is applied at the point ?

6. Conservation of Angular Momentum
In terms of angular velocity
Analogous rotational Newton’s 2nd Law
Conservation of Angular Momentum
If there is no net external torque on a system, then the angular momentum is constant.

7. Merry-Go-Round
A merry-go-round is similar to a circular disk with a mass of 100kg and a radius of 2.0m. It is rotating at 1.57 rad/s when a stationary man of mass 70kg jumps on the edge. What is the new angular velocity?
The man now moves to within 1.0m of the center. Now what is the angular velocity

8. Conservation of Angular Momentum
Orientation of earth is maintained
Plane of earth’s orbit is maintained.
Ex. Gyroscope
Eq.
N.P.
Sun
S.P.

9. Angular Momentum
For a particle, angular momentum is calculated by the formula
Ex. What is the angular momentum of the Halley’s Comet at perihelion?
What happens to Halley’s
Comet as it swings away
from the sun?