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A cheat sheet for physics students to help in mechanics chapter
Typology: Cheat Sheet
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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 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
, radius r
Force, Newton's Laws:
Newton's 2
nd
law:
net
i= 1
n
i
=m ⃗a
1 Newton= 1 N= 1
kg m
s
2
Newton's 3
rd law:
AB
BA
Hooke's law: F^ x
=−k x (^) for spring with spring constant k
Friction: static f^ s
s
n
directed against the direction of motion
kinetic f^ k
k
n
s
k
; rolling f^ r
r
n
Center of Mass: ⃗r^ CM
r dm (^) , ⃗F net, ext
i= 1
n
i , ext
=M ⃗a CM
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
Potential Energy U =−W , (^) dU =−F⋅d
l Conservative force^
x
dU
dx
Energy Conservation E sys
mech
therm
chem
other
with E mech
sys
sys
sys
in
out
Momentum p=mv^ Newton's 2
nd F net ext
d
sys
dt
Impulse
sys
t i
t f
sys
dt=Δ ⃗p
Collision: coefficient of restitution e=^
v recession
v approach
is between 0 (perf. inelastic) to 1 (elastic)