The Truss
Internal forces in simple structures Example: the truss
Serway 12.3 Lab Manual, Lab D4
Practice: Serway chapter 12, problems 37, 49, 54
Physics 1D03 - Lecture 18
Two-Force Members Member in tension B D B D
forces on member
forces by member
Mem

Harmonic Motion (II)
Mass and Spring Energy in SHM
Serway 15.115.3
Practice: Chapter 15, problems 9, 15, 17, 19, 21, 67
Physics 1D03
Simple Harmonic Motion
SHM:
x = A cos( t + )
v= dx dv , a= dt dt
differentiate:
and find that acceleration is proportiona

Simple Harmonic Motion
Serway Chapter 15.1, 15.2
Practice: Chapter 15, problems 5, 7, 11
Oscillatory Motion
Motion in the real world may not fit some of our earlier models (linear or circular motion, uniform acceleration). Many phenomena are repetitive or

Angular Momentum III
Examples with conservation of angular momentum General motion of a rigid body Collisions involving rotation
Serway 11.4
Practice: Chapter 11, problems 30, 36, 39, 41, 51, 53, 63
Physics 1D03
Collisions: Collisions can conserve angul

Angular Momentum 2
Angular momentum of a particle
Text sections 11.2 - 11.4
Practice Problems: Chapter 11, problems 11, 13, 15, 19, 55
Physics 1D03
Review Quiz
Two astronauts are held together by a long rope and rotate about their common center of mass.

Angular Momentum
Angular momentum of rigid bodies Newtons 2nd Law for rotational motion Torques and angular momentum in 3-D
Text sections 11.2 - 11.4
Practice Problems: Chapter 11, problems 25, 27, 29, 34, 55
Physics 1D03
1
Angular momentum is the rotati

Rolling Motion
Combined translational and rotational motion Rolling without slipping Dynamics of rolling motion
Text Section : 10.9
Practice problems: Chapter 10, problems 55, 57, 76, 77
Physics 1D03
1
The general motion of a rigid body (i.e., not pure r

Centre of Mass
Definition (review) Total momentum of a system of particles Motion of the centre of mass Serway 9.5, 9.6, 10.9
For practice: Chapter 9, problems 41, 43; Chapter 10, problem 73
Physics 1D03
Review: Newtons Second Law
For a particle: (Net ex

Collisions (II)
Momentum and Kinetic Energy in Collisions
Serway 9.3, 9.4
For practice: Chapter 9, problems 21, 27, 59, 66
Physics 1D03
4
Elastic Collisions
In one dimension (all motion along the x-axis): 1) Momentum is conserved:
m1v1i + m2 v2i = m1 v1f

Collisions
Conservation of Momentum Elastic and inelastic collisions
Serway 9.3 - 9.4
For practice: Chapter 9, problems 5, 19, 25, 29, 35
Physics 1D03
2
Momentum: p = mv Impulse (a vector) is defined as F t (for a constant force), or
F dt
dp dt
in gener

Momentum
Newtons original quantity of motion a conserved quantity a vector Today: -momentum and impulse -Newtons Second Law in another form Serway 9.1 9.3
Practice problems: Chapter 9, problems 1, 11, 15, 17
Physics 1D03
Definition: The linear momentum p

Energy
Examples with rotation Force and Potential Energy
Serway 7.8, 7.9; 10.8
Practice problems: Serway chapter 7, problems 47, 51, 52; chapter 10, problems 49, 51, 52, 53, 67
Physics 1D03
Rotation about a fixed axis
Kinetic Energy:
K = I 2
Work:
dW = d

Mechanical Energy
More examples Non-conservative forces
Serway 8.1 8.4
Practice problems: Serway chapter 8, problems 7, 15, 23, 65, 69
Physics 1D03
Mechanical Energy E = K + U = K + Ugravity + Uspring + .
Mechanical energy is conserved by conservative fo

Power; Rotational Energy
Power Rotational work, power, and kinetic energy. Serway 7.5, 8.5, 10.4, 10.8
Suggested Problems: Chapter 8, problem s 31, 39 Chapter 10, problems 25, 27, 47, 49, 52, 53.
Physics 1D03 - Lecture 21
Power
Power is the rate at which

Work and Kinetic Energy
Kinetic Energy and the Work-Energy Theorem
Serway 7.4, 7.5
Suggested Problems: Chapter 7, problems 27, 31, 33, 39
Physics 1D03
Varying force:
Work is the area under a graph of force vs. distance (include only the force component pa

Work and Energy
Newtons approach:
F = ma
r
r
- acceleration at any instant is caused by forces
Energy approach: Net work = increase in kinetic energy
- equivalent to Newtons dynamics - scalars, not vectors - compares energies before and after
Work: Serwa