bring: student card mcmaster standard calculator pen and pencil … · 2014-10-03 · physics 1d03...
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Physics 1D03
Bring:
student cardMcMaster standard calculator
pen and pencilYou must write in the correct room
No mobile phones, music players, etc. in the test room.
No notes are permitted.
The standard formula sheet (posted on avenue) will be
provided with the exam paper.
Answers to the multiple-choice must be written in pencil.
Solutions to the problems may be written in pen or pencil.
Physics 1D03
J. P
. Student
version number
from front of test
Multiple-choice answer sheets:
HB pencil only; ink will not work
Fill circle completely
No extra marks in answer area
Erase well to change an answer
student number
coded for scanner
Physics 1D03
Review for Test 1
What topics usually give students trouble?
� Vector Components� Free-body Diagrams� What is a force? What is acceleration?
� Newton’s Third Law
� Circular motion and F=ma
� What are angular velocity, angular acceleration, etc.?
Physics 1D03 - Lecture 4
A vector can be written in terms of its components:Ar
kjiArrrr
zx AAAy
++=
i
j
Ar
Ax i
Ay j
Ay j
Ax i
Ar
Physics 1D03 - Lecture 5
Acceleration is the
rate of change of
velocity :)(tv
r
)( ttv ∆+r
t time
tt ∆+ time
path of particle
)(tvr
)( ttv ∆+r
vr
∆t
va
∆
∆≈
rr
t
v
t ∆
∆≡
→∆
r
lim 0
dt
vda
rr
≡
Physics 1D03 - Lecture 8
Free-Body Diagrams
• Pick one object (the “body”).
• Draw all external forces which act directly on that body
(gravity, contact, electromagnetic). Imagine cutting around the body to separate it from its surroundings.
Replace each external object with a force applied at the point of
contact.
• Indicate the direction of the acceleration of the object
beside the diagram; but remember, ma is not a force.
Physics 1D03 - Lecture 8
Example: free-body diagram
A block is pulled up a frictionless ramp:
m
Note :
• title, to indicate the chosen
object
• contact forces, to replace the
rope and the ramp
• gravity doesn’t require contact
• a may be indicated for
reference, but is not a force
gmr TF
r
nr
ar
Forces on Block
Physics 1D03 - Lecture 9
Doing problems with “F=ma”
• Draw the free-body diagram carefully.
• You may need to know the direction of a from
kinematics, before considering forces.
• Any axes will do, but some choices make the algebra
simpler.
• You need one (scalar) equation for each (scalar)
unknown, in general (but, note the mass cancelled out
in the previous problem).
Physics 1D03 - Lecture 10
Problems with several accelerated objects:
• Free-body diagram for each object.
• Relate forces by finding action-reaction pairs, etc.
• Look for constraints on the motion to relate accelerations.
• “F=ma” for each diagram, break into components.
• Count unknowns: do you have enough equations?
• Use algebra to solve.
Physics 1D03 - Lecture 7
Newton’s Third Law (action and reaction)
Whenever object A exerts a force on object B,
object B simultaneously exerts an equal,
opposite force back on A.
Physics 1D03 - Lecture 10
Review: Circular Motion Kinematics
has components ar
directionin change from , ii)
of change of rate , i)
2
r
va
dt
vda
r
t
=
= speed
r
centertangential component,
radial component,
ta
ra
ar
Physics 1D03 - Lecture 10
Particle dynamics : nothing new• There is no “centrifugal force”
•
• has a radial component
component as well as
(perhaps) a tangential
component
amr
forces) (real∑ =
ar
Centrifugal
Force
Physics 1D03 - Lecture 10
( )
( ) ( )
( ) ( )tdt
dt
tdt
dt
t
ωα
θω
θ
=
=
angle (“theta”):
angular velocity (“omega”):
angular acceleration (“alpha”):
0 θ reference axis
(radians)
(rad/s)
(rad/s2 )
Physics 1D03 - Lecture 10
22
ωrr
var ==
The tangential component at is equal to the rate of increase of speed. There is also a radial (centripetal) component, due to the change in
direction of v:
θrs =
ωrvt =
αrat =
ar
at
Pa
These relations require angular quantities to be measured in
radians (or rad/s, etc.).
Physics 1D03 - Lecture 10
if t ωαω +=
iif tt θωαθ ++=2
21
for constant α only !
These expressions are should remind you of relations for constant linear acceleration: θ replaces x, ω replaces v, α replaces a.
Constant angular acceleration:
Physics 1D03 - Lecture 10
Angular velocity vector: parallel to the axis
of rotation, following a similar right-hand rule:
Angular acceleration vector: parallel to the
angular velocity, if |ω| is increasing.
ωωωω rotation
direction
ωωωω