Mon, Mar 29

A4 - 23 days - ends Apr 28

• Review - Work:
  • Ch 8 (p. 262) #109-115odd
  • Ch 9 (p. 298) #37, 39, 43, 45 (Note: The y-axis passes through m₁ and m₃, not m₁ and m₄.), 47

Ch 9 Rotation

• 9-3 Calculating the Moment of Inertia
• Rotational inertia of a particle
  • I_particle = mr²
• Rotational inertia of a system of particles
  • 
• Rotational inertia of an extended body
  • 
• Parallel Axis Theorem: I = I_cm + Mh²
• Moment of Inertia of Common Shapes (Table 9-1, p. 274)
• 9-4 Newton's Second Law for Rotation
  • Torque - "turning force"
    • depends on:
      • amount of force
        • more force more rotational acceleration
      • direction of force
        • force perpendicular to radius - maximum acceleration
        • force parallel to radius - no acceleration
      • where the force is applied
        • more radius - more rot. acceleration
    • Calculating torque
      • (see Fig. 9-18 p. 280)
      • Actually
        • direction: right-hand rule (torque is an axial vector)
        • in problem solving, counterclockwise is +, clockwise is - (by convention)
      • Even though torque has units N^.m, torque is not measured in Joules - torque is a vector, work is a scalar.
      • Torque = force times "lever arm"
        • 
  • Newton's Second Law:
• 9-5 Applications of Newton's Second Law for Rotation
  • Note: You have to account not only for all of the forces on an object, but where on the object the forces are applied
• Rod pivoted at one end (see examples 9-6 and 9-9)
• Accelerating a flywheel (see example 9-8)
• Massive pulleys (see examples 9-10 and 9-11)

• Read and Study:
  • 9-4 and 9-5
• Work:
  • Ch 9 #68-71, 73
  • Answers: 68) (a) v = 3.95 m/s, (b) 49.3 rad/s 70) v = 2.79 m/s, = 34.9 rad/s

• Catch up on your assignments.

9-6 Rolling Objects

• "Rolling without slipping" concepts
  • the role of friction
  • motion of:
    • the point of contact between the wheel and surface
    • the center of the wheel
    • the top of the wheel
  • rotation about:
    • point of contact
    • center of the wheel (rotation + translation)
• Kinetic energy of a rolling object
  • 
• Objects rolling up and down inclines
  • Who wins the race between a disk, a sphere, and a hoop?
  • Conservation of Energy approach
  • Newton's Second Law approach (What is the friction force?)
• Rolling with slipping - the bowling ball problem
  • initial conditions - the effect of friction
  • time for which

• Read:
  • 9.6
• Work:
  • Ch 9 #79-87odd

Fri, Apr 2

Chapter 10 Conservation of Angular Momentum

• 10-1 The Vector Nature of Rotation (review for us)
  • Right-hand rule
  • Cross product
• 10-2 Torque and Angular Momentum
  • Angular Momentum, L, of a particle
    • For a particle moving in a circle, p = mv, so we would like .
    • In general,
    • direction of L - use right-hand rule

    • Linear	Rotational
      (see note 1)	(see note 2)

    • Note 1: This is Newton's Second Law:
    • Note 2: This is Newton's Second Law for Rotation:

• Read:
  • 10-1 and 10-2
• Answer:
  • Ch. 10 #1-9odd, 43-46
  • Answers: 44a) 28.0 kg m²/s, 44b) 32 kg m², 44c) 0.875 rad/s

Ch 10 Conservation of Angular Momentum

• 10-3 Conservation of Angular Momentum
  • From Newton's 2^nd Law for Rotation: , so if the net torque on an object (system) is zero, the rate of change of its angular momentum will be zero.
  • In other words, if the net torque on a system is zero, its angular momentum will not change.
    • Skaters and divers
• Conservation of Angular Momentum in a bicycle wheel
• Vector nature of angular momentum
• Summary of Linear and Rotational Dynamics Equations

• Read:
• 10-3
• Work:
  • Ch 10 #12, 49, 51, 55, 57

Ch 11 Gravity

• 11-1 Kepler’s Laws
  • First Law - Orbits are ellipses with sun at one focuw
  • Second Law - Radius vector sweeps out equal areas in equal times
• Third Law - T² = kr³
  • mean distance = length of semi-major axis
• 11-2 Newton’s Law of Universal Gravitation
  • Derivation of Kepler's Laws
• 11-3 Gravitational Potential Energy
• Using a graph of gravitational potential energy
• Escape energy
• Escape velocity
• Energy in a circular orbit
• 11-4 The Gravitational Field and g
  • g as a measure of gravitational field strength

• Read:
• Ch 11
• Work:
  • Ch 11 #1-9odd, 15, 17, 21, 23, 37, 43-49odd, 53, 57, 59

• Finish the Ch 11 assignment

Ch 12 - Static Equilibrium

• Conditions for static equilibrium:
  • F_net = 0 in both the x and y directions
  • about any axis
• Examples

• Read:
  • 12-1 - 12-3
• Work:
  • Ch 12 #1, 2 (ans: false), 9, 14 (ans: 1.4 m), 28 (ans: (a) Forces are T₁, T₂, and F_H, (b) 139 N), 49

Ch 14 Oscillations

• Simple Harmonic Motion (SHM)
  • If the net force on an object is a Hooke's Law force (F_net = -kx), the object will move in simple harmonic motion.
  • 
  • Where:
• SHM and circular motion
• Examples

• Read:
  • 14-1
• Work:
  • Ch. 14 #1, 3, 23-27 odd

Ch 14 Oscillations

• 14-2 Energy in SHM
• 14-3 Some Oscillating Systems
  • The simple pendulum
  • The physical pendulum

• Read:
  • 14-2 and 14-3
• Work (The last assignment in AP Physics):
  • Ch 14 #57, 60. 61, 67

Wed, Apr 28

End of A4 - 20 days