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