Topic 1 Angular Measure

(a)    Define θ, ω, and α

(b)    Express the four most commonly used linear kinematic relationships in terms of their angular counterparts

Topic 2 Centripetal Motion

(a)   Show that the radial acceleration in uniform circular motion is equal to the product of the tangential and angular velocities.

(b)   Show that

Topic 3 Moment of Inertia

Define

(a)    Torque

(b)    Moment of Inertia

Topic 4 Angular Momentum

Show that, given Newton's laws of motion, angular momentum must be conserved in any interaction, where angular momentum is given by

Topic 5 Tops

Explain qualitatively the precession of a gyroscope.

( This question Removed because we didn't discuss this in class.) 

Playground Examples

An Merry-Go-Round in the park is set into motion by 2 neighborhood children each pushing with a force of 100 N on the edge of the Merry-Go-Round 3 m from the axis of rotation. After pushing for 80 s, they find themselves running at 3 m/s. They decide it is going fast enough and so they jump on. Each of the children have a mass of 25 kg.

Find: (a)  What is the rotational speed of the Merry-Go-Round when they jump on?
(b) What was the angular acceleration of the device?
(c) What torque did the children apply?
(d) If you were to neglect friction, what would be the moment of inertia of the Merry-Go-Round?
(e) How much do the children add to this moment of inertia when they jump on?
(f) Once the children are on the Merry-Go-Round, they will see the horizon seem to be tilted due to the inertial force. How great is that inertial force in terms of the acceleration due to gravity?

Textbook Problems