Lectures 32-34
Example: At position 1 the skier is moving at 20 m/s. When he reaches position 2,
20 m below position 1, he jumps upward with vertical component of velocity of
3 m/s. (Ignore friction a
APPLIED MATHEMATICS 1B: MATH142
December 2016
1. Some formulae you may nd useful.
(a) Mass moments of inertia of homogeneous objects.
1
(i) Rod of mass m and length l about an endpoint: 13 ml2 , about
Lectures 28-29
14.3 Curvilinear motion - normal and tangential components
Example: The mass of a solar powered car and the driver is 100 kg. The car starts from
rest on the track at , moving to the ri
Lectures 44-45 (final)
Chapter 18: Kinetics of rigid bodies
We now include the forces that cause the motion of a rigid body.
Equations of motion for a rigid body
(a) Translational
Object - regarded as
Lectures 25-27
Example: Due to the rotation of the forked rod the ball
travels around the slotted path. A portion of path is in the
shape of the cardioid
= 0.5 1 cos
m .
If the ball's speed is = 1.5 m
Lectures 23-24
Expressing acceleration in terms of the radius of curvature.
Page 1
Summary: Normal and tangential components of velocity and acceleration.
Example: Helicopter starts from rest at = 0.
Lecture 16
Chapter 13: Kinematics of a particle
Read through section 13.1
13.2 Straight-line (rectilinear) motion
Straight line path of a point is defined using a single coordinate axis .
Page 1
Examp
Lectures 21-22
(b) Determine the number of revolutions the rotor turns as it decelerates from
10 000 rpm to 1 000 rpm.
Page 1
Derivative of a rotating unit vector w.r.t. time
Page 2
Page 3
13.6 Curvil
Lectures 35-36
Chapter 16: Momentum Methods
Used to
find change in velocity when the external forces are functions of time,
analyse impacts between objects.
16.1 Principle of impulse and momentum
Pa
Pietermaritzburg Campus
MODULE COURSE INFORMATION SHEET - 2016
MODULE CODE: MATH142
MODULE NAME: APPLIED MATHEMATICS 1B
LECTURERS
Module Coordinator
Dr. JM T. Ngnotchouye
Lecturer
Dr. JM T. Ngnotchouy
Lectures 19-20
13.4 Curvilinear motion - Cartesian coordinates
Straight-line motion - use scalars ,
and .
Motion of a point described by a curvilinear path relative to some reference
frame - use vecto
Lectures 41-43 (final)
Example: The 4 kg disc slides on the smooth
horizontal surface. It is attached to an ideal string
being pulled through hole at constant velocity
= 0.02 m/s. Initially = 0.5 m an
Lectures 46-47 (final)
Example: The slender bar (mass , length ) is released from rest in the
position shown. Find the bar's angular acceleration and the components of the
reaction force exerted on th
Lectures 39-40 (final)
(b) What fraction of the kinetic energy before impact is lost during impact?
16.3 Angular Momentum
Principle of angular impulse and angular momentum
(a) Vector form: Consider an
Lectures 37-38
Impacts
Bodies interacting with each other over a very short period of time.
Characterized by very large impulsive forces.
Direct central impact
COM's of
impact.
and
move on a straig
Lectures 48-49 (final)
Example: A sphere (mass , radius ) is projected onto a horizontal surface with
initial velocity
and zero initial angular velocity. The coefficient of kinetic
friction is .
Find
Lectures 30-31
Evaluating the work done
Page 1
Notes:
(a) The components of the force normal to the path do no work.
(b) If
is opposite to the direction of motion, then the work done is negative.
(c)
Lectures 50-51 (final)
Example: A solid sphere (mass , radius ) is
released from rest. If the sphere rolls without
slipping, find the speed of its centre when it has
moved a distance down the incline.
Introduction to Engineering Materials
Test 1, 2010
Marks: 66 Duration: 45 minutes
NOTE
- Select the single most correct answer per question.
- Ring your answer on the test question sheet AND block it
Introduction to Engineering Materials
Test 2, 2010
Marks: Duration: 45 minutes
NOTE
Select the single most correct answer per question.
Ring your answer on the test question sheet AND block it out i
University of KwaZulu-Natal Main Examination
Applied Mathematics 1B
13 November 2015
1
Math 142
PART 1
From the 5 dierent possible answers given choose the correct answer(s), and write the correspondi
Mathematics 1A
August 21, 2015
Test 1
The following formulae may be useful.
Centroids.
(i) Semi-circular area: on the axis of symmetry at a distance of
4R
3
from the diameter.
(ii) Solid right-circul
ENGINEERING APPLIED MATHEMATICS 1B
4 October 2013
Quiz Test 2
Maximum Marks: 25
1. A particle travels along the positive xaxis with its speed (in m/s) represented by the vt
graph below (note that the
APPLIED MATHEMATICS 1B: MATH142
November 2014
1
1. Some formulae you may nd useful.
(a) Mass moments of inertia of homogeneous objects.
1
(i) Rod of mass m and length l about an endpoint: 13 ml2 , abo
APPLIED MATHEMATICS 1B: MATH142
November 2013
1
1. Some formulae you may nd useful.
(a) Mass moments of inertia of homogeneous objects.
(i) Rod of mass m and length l: about an endpoint 13 ml2 , about