Physics 313 (Mechanics) Formula sheet
Motion in 1 dimension:
Duration, Displacement:
x=xf−xi
,
t=tf−ti
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.
,
xt=x0v t
Motion with constant acceleration:
a=aav=const.
,
vt=v0a t
,
xt=x0v0t1
2a t 2
vav=vi+vf
2
,
vt2=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
fssFn
directed against the direction of motion
kinetic
fk=kFn
,
sk
; rolling
fr=rFn
Center of Mass:
rCM=1
M∫r dm
,
Fnet, ext=∑
i=1
n
Fi , ext=MaCM
Work
W=∫
1
2
F⋅d
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 =−
F⋅d
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)