CHEAT SHEET - SpoonFeedMe

CHEAT SHEET

PHYS1205: Integrated Physics

Final Displacement with Avg. Velocity

Vector Multiplication/Division by a Scalar ¨C Only

magnitude is multiplied or divided. Direction is

reversed for negative scalars.

1

?! = ?! + ? (?!" + ?!" )?

2

University of Newcastle

Final Displacement with Velocity and Acceleration

1

1D Motion

Vector ¨C A measurement with both magnitude and

direction (e.g. Displacement)

Scalar ¨C A measurement with only magnitude (e.g.

distance)

1

?! = ?! + ?!" ? + ?! ? !

2

Vector Components

?

Length

? =

Final Velocity without Time

!

!

?!"

= ?!"

+ 2?! ?! ? ?!

?

??

??

Objects in Freefall ¨C Acceleration is ¨Cg (9.8m/s )

Instantaneous Velocity

?!"#$

2

Vectors and 2D Motion

Vector Addition ¨C Tip to Tail

??

=

??

? = ? tan!!

??

??

Instantaneous Acceleration

?!"#$ =

??

??

Final Velocity

?!

? = ? x? + ? y?

Projectile Motion

?

Vector Subtraction ¨C From the negative to the

positive, or add the negative (? ? ? = ? + (??))

?!

Unit Vectors:

Position

1

?! = ?! + ?! ? + ?? !

2

Average Acceleration

?!"# =

!

Direction

2

Average Velocity

?!"# =

!

?! + ?! ?

?

Initial Horizontal Velocity

?!" = ?! cos ?

?

Initial Vertical Velocity

?!" = ?! sin ?

?!" = ?!" + ?! ?

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Uniform Circular Motion

?

Equilibrium

?

Kinetic Energy

Kinetic Friction

?? =

? = ?! ?

!

?! + ?!

!

?

?? = ???

? ¡Ü ?! ?

2??

?

?!

? = ??! = ?

?

?!" = ?!" + ?!" ?

Force and Motion

st

Newton¡¯s 1 Law - In the absence of external forces,

when viewed from an inertial reference frame, an

object at rest will remain at rest and an object in

motion continues in motion with a constant velocity

?? = ??

4

?!" = ? ??!"

Gravitational

? = ????

Elastic

Work, Energy and Power

Scalar/Dot Product

? ? ? = ??????

Work

?

Same Direction as Displacement

? = ???

?

Different Direction to Displacement

?=

?

Non-conservative Force - Work done dependent on

the motion of the object (e.g. Friction)

Conservation of Energy

?

?!"# =

!!

!!

Mechanical Energy

?!"#! = ?? + ?

?

Work by Varying Force

1 !

??

2

Conservative Force - Work done is independent of

the path taken by an object (e.g. Gravity)

? = ???????

rd

Newton¡¯s 3 Law - If two objects interact, the force

that object one is exerting on object 2 is equal and

opposite to that object two is exerting on object one

?

?

nd

Newton¡¯s 2 Law - Net Force is the product of Mass

and Acceleration

Potential Energy

Circular Motion Dynamics

Relative Velocity

1

?? !

2

Work-Kinetic Energy Theorem

Static Friction

Period

?=

3

?! = ???

Friction

?!

?

Overall Acceleration

|?| =

?

?? = 0

Centripetal Acceleration

?! =

?

Hooke¡¯s Law

Total Energy

?!"! = ?? + ? + ?!"#

?! ??

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?

Non-Conservative Force Absent

?

Conservation of KE (Elastic Collisions)

??!"#! = 0

?

??! = ??!

Non-Conservative Force Present

?

Perfectly Inelastic

??!"! = 0

?! ?!! + ?! ?!! = (?! + ?! )?!

Power

?

??

?=

??

5

Perfectly Elastic

?! ?!! + ?! ?!! = ?! ?!! + ?! ?!!

1

1

1

1

? ?! + ? ?! = ? ?! + ? ?!

2 ! !! 2 ! !! 2 ! !! 2 ! !!

Momentum

6

? = ??

Definition

Final Angular Displacement

?! = ? ¦È! + ¦Øt + ¦Át !

Final Angular Velocity without Time

¦Ø!! = ?!! + ?2¦Á(¦È! ? ¦È! )

1

¦È! = ¦È! + (¦Ø! + ¦Ø! )t

2

Arc Length

Kinetic Energy of Rotation

?! = ?

Translational Velocity

For Constant Force

For Non-Constant Force

?=

!!

? = ??

Translational Acceleration

? = ??

?. ??

!!

?

? = ?

Average Angular Velocity

?!"#

Conservation of Momentum (All Collisions)

?! = ?!

?????

??

=

??

Instantaneous Angular Acceleration

?! ?!!

General

? = ??

??

=

??

?!

2

Moment of Inertia

?

Instantaneous Angular Velocity

Collisions

?

?! = ?! + ?¦Át

? = ??

? = ??

?

Final Angular Velocity

Rotation

Impulse

?

??

??

Final Angular Displacement with Avg. Velocity

Momentum

?

?!"#$ =

?

?? ! ???

Sphere

?=

2

?? !

5

?=

1

?? !

2

Cylinder

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?

7

Disk

? = ?? !

Parallel Axis Theorem

Waves, Oscillations and SHM

Wave Number

?

?!"#! =

Wave Equation

Torque

?

? = ? ¡À? ?! ? ? !

? = ??????

?

Using Perpendicular Distance

?

?=

Net Torque

?? = ??

and

?! = ??

?

?

?

? = 2?

General Equation

Acceleration

Angular Momentum

?

???

? = 2?

?! = ?? ! ?

?

Angular Frequency

The Conservation of Momentum

?=

?! = ?!

?

?

?

Period

Frequency

8

Sound and EM Waves

Bulk Modulus

?=?

?=

?

?

?

Physical Pendulum

o

? ? = ????(?? + ?)

?

? = ??

?

?

?

SHM and Circular Motion ¨C Uses SHM

formulae for each direction of movement

SHM and the Pendulum

o Period

Simple Harmonic Motion

!

Angular Momentum

?

Speed of Wave on a String

? = ??

1 !

??

2

Velocity

? ?, ? = ???? ?? ? ?? + ?

Using Radius

?

1

=

2? ?

Energy

2?

?=

?

? = ?!" ¡Á?? !

?

?=

2?

?

??

??/?

Sound Wave Displacement

? ?, ? = ?!"# cos ?(?? ? ??)

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Sound Wave Pressure

?

?

Including Bulk Modulus

?=

?? = ??!"# sin ?(?? ? ??)

?

?

Without Bulk Modulus

?¡Ô

Formula

?????!"#

4?? !

? = 2???? ?? cos ?(??)

?

Amplitude

??? = 2????(??)

?

? + ?!

?

? ? ?!

?

?!

273

?

?

EM Waves

?

Electrical Component

? = ?! sin ?(?? ? ??)

Magnetic Component

? = ?! sin ?(?? ? ??)

When a pulse hits a fixed boundary, reflection

is inverted

When a pulse hits a free boundary, reflection

is not inverted

When a pulse moves from a light to a heavy

string the reflected pulse is inverted

When a pulse moves from a heavy to a light

string, the reflection is not inverted

? = 2???? ?? ? ?? +

?

?

cos

2

2

??

?(????? ?? = 0, 1, 2 ¡­ )

2

Antinodes

??

?????? ?? = 1, 3, 5 ¡­ )

4

Boundary Conditions on a String

?! =

? ?

2? ?

Standing Waves in an Air Column

?

Superposition

Interference

Nodes

?=

Reflection of a Pulse

?

Intensity of a Sound Wave

Formula

?=

?¡ä =

Dependence on Temperature

? = ?331 1 +

?

?

Doppler Effect

?

? = ?

?

?

Standing Waves on a String

?

? = 10 log

?!

Speed of Sound

?

!

Sound Levels in Decibels

?

?=

?

?

??!"#

2??

In Three Dimensions

??!"# = ????!"#

Density

???? ???????????

¡Á2? = ????? ???????????

?

Per Unit Area

Closed Pipe

?! =

?

??

?(????? ?? = 1, 3, 5 ¡­ )

4?

Open Pipe

?! =

??

?(????? ?? = 1, 2, 3 ¡­ )

2?

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