Review for Test

1
Review for Test 4

• Responsible for - Chapter 12, chapter
  14 (except 14.7 and 14.8), sections 10.7 and
  13.5 as well as Chapters 1-11 - Problems worked
  in class and notes - Homework assignments
• Test format - Three problems, 30 pts
  each - Set of conceptual questions, 10
  pts - Time 75 minutes
• Test materials - Pencil, eraser, and
  calculator - No formulae sheet or paper,
  Closed text and notes

2
Material Covered

• Chapter 12Rotational Dynamics - Torque,
  Newtons 2nd Law ??I? - Moment of inertia,
  integral relation - Rotational work and
  kinetic energy - Conservation of Energy with
  rotation - Rolling motion (tire) -
  Angular momentum - Conservation of angular
  momentum - Vector product, vector nature of
  quantities
• - Static Equilibrium - applications of
  ??0, ?F0 - center of gravity

3
Material Covered (contd)

• Chapter 14 Oscillations - Simple harmonic
  motion (SHM) - Spring-mass system as SHM -
  Simple pendulum, physical pendulum -
  Differential equation version, solution -
  Initial conditions, phase constant, amplitude -
  Energy for SHM
• Potential energy curves - equilibrium
  points, potential slope (10.7) - gravitational
  potential energy (13.5) - orbital energetics
  (p. 401)

4
Example Problem
A pendulum of length L and mass M has a spring
with a force constant k connected to it at a
distance h below its point of suspension (drawing
to be provided). Find the frequency of vibration
of the system for small values of the amplitude
(small ?). Assume the vertical suspension of
length L is rigid, but ignore its mass.
Solution Apply Newtons second law for
rotation. Make small angle approximation Write
in the form of a differential equation Extract
?
5
Example Problem
(a) What is the minimum speed, relative to the
Sun, necessary for a spacecraft to escape the
solar system if it starts at the Earths orbit?
(b) Voyager 1 achieved a maximum speed of 125,000
km/h on its way to photograph Jupiter. Beyond
what distance from the sun is this speed
sufficient to escape the solar system? Solution
Apply conservation of energy and gravitational
potential energy To just escape the sun, the
spacecraft must have a potential energy at R?? of
zero
6
Example Problem
A 0.200-m bar with a mass of 0.750 kg is released
from rest in the vertical position. A spring is
attached, initially unstrained, and has a spring
constant of 25.0 N/m. Find the tangential speed
with which the free end strikes the horizontal
surface. (drawing to be provided) Solution Bar
rotating with axis at one end ? rotational KE, no
translational KE Bar falls from some height ?
gravitional PE (Ug) A spring is attached to bar ?
spring PE (Us) Bar ? rigid body ? need moment of
inertia ? Use Conservation of Energy
7
yi?h since this would mean all mass of rod is at
yih, but mass is distributed. So, take mass to
be located at center of gravity
8
From geometry of problem
Return to Conservation of Energy and solve for vt