Physics 124 formula sheet PDF

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Physics 124 formulas...

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Physics 124 Data Sheet Displacement: ∆𝑥 = 𝑥! − 𝑥"

Average Speed: 𝑣 =

Instantaneous Speed: |𝑣 |

# $

Average Velocity: 𝑣%& =

∆( ∆$

=

Average Acceleration: 𝑎%& =

Instantaneous Velocity: 𝑣 = lim

(! )("

∆& ∆$

=

∆(

∆$→+ ∆$

$! )$"

Instantaneous Acceleration: 𝑎 = lim ∆$

&! )&"

∆&

$! )$"

Equations of motion: (𝑎,&,𝛼,𝑐onstant)

∆$→+

𝑣( = 𝑣+( + 𝑎( 𝑡

𝑣, = 𝑣+, + 𝑎, 𝑡

𝜔 = 𝜔+ + 𝛼𝑡

𝑥 = 𝑥+ + . (𝑣+( + 𝑣( )𝑡

𝑦 = 𝑦+ + . (𝑣+, + 𝑣, )𝑡

𝜃 = 𝜃+ + . (𝜔+ + 𝜔)𝑡

𝑥 = 𝑥+ + 𝑣+( 𝑡 + 𝑎( 𝑡 .

𝑦 = 𝑦+ + 𝑣+, 𝑡 + 𝑎, 𝑡 .

𝜃 = 𝜃+ + 𝜔+ 𝑡 + 𝛼( 𝑡 .

. 𝑣(. = 𝑣+( + 2𝑎((𝑥 − 𝑥+)

. 𝑣,. = 𝑣+, + 2𝑎,(𝑦 − 𝑦+)

𝜔. = 𝜔+. + 2𝛼 (𝜃 − 𝜃+ )

-

-

-

-

-

.

-

.

.

Projectile Motion: Horizontal launch: Time of Flight: 𝑡 = < 0

Range: 𝑣+ <

./

./ 0

If the initial & final elevations are the same: Time of Flight: 𝑡 =

Range: =0# > sin 2𝜃 &%

.&#$ 0

Maximum range (when sin 2𝜃 = 1 or 𝜃 = 45°):

𝑅123 =

&#% 0

Newtons Laws of Motion: Newton’s Second Law: Weight: Hooke’s Law: Kinetic Energy: Kinetic Friction: 𝑓6 = 𝜇6 𝑁

𝐹45$ = 𝑚𝑎 𝑊 = 𝑚𝑔

𝐹( = −𝑘𝑥

𝐾 = . 𝑚𝑣 .

Centripetal Acceleration:𝑎:; = Gravitational: 𝑈 = 𝑚𝑔𝑦

-

&% <

Static Friction: 𝑓7,9%( = 𝜇7 𝑁 Centripetal Force: 𝑓:; = 𝑚𝑎:; = Spring: 𝑈 = . 𝑘𝑥 . -

9& % <

𝑊$=$%> = ∆𝐾 = 𝐾! − 𝐾"

Work-Energy Theorem: Work: 𝑊 = 𝐹𝑑

𝑊 = . 𝑘𝑥 . -

𝑊 = 𝐹𝑑 cos 𝜃

𝑊:=475 0

Average Angular Velocity: 𝜔%& =

Clockwise = 𝜃 < 0

Instantaneous Angular Velocity: = 𝜔 lim

∆@ ∆$

∆$→+ ∆$

Relating Angular Velocity & Period: 𝑇 = Average Angular Acceleration: 𝛼%& = Tangential Speed: 𝑣$ =

circumference

Centripetal a: 𝑎:; = 𝜔 . 𝑟

period

∆@

=

.AB = |𝜔|𝑟 .A

Tangential a: 𝑎$ = |𝛼 |𝑟

𝜃 = tan)- =% > %'( )

Linear Speed: 𝑣 =

.A< P

= | 𝜔|𝑟

Rolling without slipping: 𝑎 = 𝛼𝑟

Rotational Kinetic Energy: 𝐾 = 𝐼𝜔 . . -

Translate and Spin: 𝐾 = 𝑚𝑣 . + 𝐼𝜔 . . . -

-

Rolling without slipping: 𝐾 = 𝑚𝑣 . =1 + 9< %> . -

Q

Moment of Inertia: 𝐼 = 𝑚" 𝑟". Torque: 𝜏 = 𝑟𝐹 sin 𝜃

𝜏 = 𝐼𝛼

Counterclockwise = 𝜏 > 0 𝜏 = 𝐼𝛼 =

Clockwise = 𝜏 < 0

RS R$

Angular Momentum: |𝐿 | = 𝑚𝑣𝑟 = 𝑟𝑝

𝐿 = 𝐼𝜔 Springs Harmonic Motion:

𝑥 = 𝐴 cos = 𝑡> = 𝐴 cos(𝜔𝑡) P

RADIANS

𝑡=0

𝑥 = 𝐴 cos =P ∗ 0> = 𝐴 cos (0) = +𝐴

(START OF CYCLE)

𝑡=

𝑥 = 𝐴 cos =P ∗ T> = 𝐴 cos =U> = +0.707𝐴

.A

Displacement:

𝑡= 𝑡= 𝑡=

.A

.A

P T

P

A

𝑥 = 𝐴 cos =P ∗ U> = 𝐴 cos =.> = 0 .A

P U

P

A

𝑥 = 𝐴 cos =P ∗ .> = 𝐴 cos(𝜋) = −𝐴 .A

P .

P

𝑥 = 𝐴 cos =P ∗ U > = 𝐴 cos =. > = 0 .A

VP U

𝑡=𝑇

VP

VA

𝑥 = 𝐴 cos = ∗ 𝑇> = 𝐴 cos(2𝜋) = +𝐴 P .A

(ORIGIONAL POSITION)

Velocity: 𝑣 = −𝜔𝐴 sin(𝜔𝑡)

𝑣9%(B = 𝜔𝐴

Acceleration: 𝑎 = −𝜔 . 𝐴 cos(𝜔𝑡) Period: 𝑇 = 2𝜋< 6 9

𝑎9%( = 𝜔. 𝐴

𝑎 = −𝜔 . 𝑥...