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Physics 313 (Mechanics) Formula Sheet, Cheat Sheet of Mechanics

A cheat sheet for physics students to help in mechanics chapter

Typology: Cheat Sheet

2020/2021

Uploaded on 04/26/2021

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Physics 313 (Mechanics) Formula sheet
Motion in 1 dimension:
Duration, Displacement:
x=xfxi
,
t=tfti
Velocity:
vav=x
t
,
vinstantaneous(t)= dx
dt
Acceleration:
aav=Δv
Δt
,
ainstantaneous(t)= dv
dt
...due to gravity:
g=9.81 m
s2
Uniform motion:
v=vav=const.
,
Motion with constant acceleration:
a=aav=const.
,
vt=v0a t
,
xt=x0v0t1
2a t 2
vav=vi+vf
2
,
vt2=v0
22ax
Motion in 2 and 3 dimensions:
Position vector
r=x
iy
jz
k
Instantaneous velocity and acceleration
v=d
r
dt
a=d
v
dt
Relative velocity of particle p relative to reference frames A and B
vpB =
vpA
vAB
“Velocity of p relative to B equals ….”
Projectile motion: (motion in x and y is independent)
ax=0
and
ay=−g
or
a=g=−g
j
v=
g t
,
r=
v0t1
2
g t2
, horizontal range:
R=v0
2
gsin 2 0
Circular motion: due to centripetal acceleration (acceleration directed towards the center)
ac=v2
r
,
at=d v
d t
, speed
v=2r
T
, radius r
Force, Newton's Laws:
Newton's 2nd law:
Fnet=
i=1
n
Fi=ma
1 Newton =1 N=1kg m
s2
Newton's 3rd law:
FAB=−
FBA
Hooke's law:
Fx=−kx
for spring with spring constant k
Friction: static
fssFn
directed against the direction of motion
kinetic
fk=kFn
,
sk
; rolling
fr=rFn
Center of Mass:
rCM=1
Mr dm
,
Fnet, ext=
i=1
n
Fi , ext=MaCM
Work
W=
1
2
Fd
l
1 Joule=1 J =1kg m2
s2
Power
P=dW
dt =
F
v
1 Watt=1 W =1kg m2
s3
Kinetic energy
K=1
2m v 2
Wtotal= K
Potential Energy
U=−W
,
dU =−
Fd
l
Conservative force
Fx=− dU
dx
Energy Conservation
Esys=Emech+Etherm +Echem +Eother
with
Emech=Ks ys+Usys
Esys=Ein Eout
Momentum
p=m
v
Newton's 2nd
Fnet ext=d
Psys
dt
Impulse
Isys=
ti
tf
Fsys dt= Δ p
Collision: coefficient of restitution
e=vrecession
vapproach
is between 0 (perf. inelastic) to 1 (elastic)

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Physics 313 (Mechanics) Formula sheet

Motion in 1 dimension:

Duration, Displacement : ^ x=^ x^ f

−x i

, ^ t=t^ f

−t i

Velocity: v av

 x

 t

, v^ instantaneous

(t)=

dx

dt

Acceleration: a av

Δ v

Δ t

, a instantaneous

(t)=

dv

dt

...due to gravity:

g =9.

m

s

2

Uniform motion: v^ =v av

=const. (^) , x t =x 0

v t

Motion with constant acceleration: a=a av

=const. (^) , v t =v 0

a t (^) , x t =x 0

v 0

t

a t

2

v av

v i

  • v f

, v t 

2

=v 0

2

 2 a  x

Motion in 2 and 3 dimensions:

Position vector (^) r =x

i y

j z

k Instantaneous velocity and acceleration^ 

v=

d (^) r

dt

a=^

d (^) v

dt

Relative velocity of particle p relative to reference frames A and B

v pB

=v pA

v AB

“Velocity of p relative to B equals ….”

Projectile motion: (motion in x and y is independent) a x

= (^0) and a y

=−g (^) or a=g =−g

j

 (^) v =g t , ^ r^ =v 0

t

g^ t

2

, horizontal range: (^) R=

v 0

2

g

sin 2  0

Circular motion: due to centripetal acceleration (acceleration directed towards the center)

a c

v

2

r

, a t

d v

d t

, speed v^ =^

2  r

T

, radius r

Force, Newton's Laws:

Newton's 2

nd

law:

F

net

i= 1

n

F

i

=m ⃗a

1 Newton= 1 N= 1

kg m

s

2

Newton's 3

rd law:

F

AB

F

BA

Hooke's law: F^ x

=−k  x (^) for spring with spring constant k

Friction: static f^ s

s

F

n

directed against the direction of motion

kinetic f^ k

k

F

n

s

k

; rolling f^ r

r

F

n

Center of Mass: ⃗r^ CM

M

r dm (^) , ⃗F net, ext

i= 1

n

F

i , ext

=M ⃗a CM

Work W =∫

1

2

F⋅d

l 1 Joule=^1 J^ =^1

kg m

2

s

2

Power P=^

dW

dt

F⋅v 1 Watt= 1 W= 1

kg m

2

s

3

Kinetic energy K^ =^

mv

2

W total

= K

Potential Energy  U =−W , (^) dU =−F⋅d

l Conservative force^

F

x

dU

dx

Energy Conservation E sys

=E

mech

+ E

therm

+ E

chem

+E

other

with E mech

=K

sys

+U

sys

 E

sys

=E

in

−E

out

Momentum p=mv^ Newton's 2

nd  F net ext

d

P

sys

dt

Impulse

I^

sys

t i

t f

F

sys

dt=Δ ⃗p

Collision: coefficient of restitution e=^

v recession

v approach

is between 0 (perf. inelastic) to 1 (elastic)