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Physics 1501: Things to Know for the Final

Uniformly accelerated motion in 2-D: (a = ax + ay is constant)

r = r0 + v0 t +12

a t2 , v = v0 + a tvav =

12

(v + v0) , v2 v20 = 2ax (x x0) + 2ay (y y0)

Projectile motion: ay = g and ax = 0 Relative velocity: vAC = vAB + vBC

Newtons laws: 1. Absence of net force ( FNET = 0), v is constant

2. F = ma

3. Reaction = action or FA,B = FB,A

Gravity: Newtons law: F =Gm1m2

r2. On Earth: F = mg with g =

GMER2E

.

Keplers 3rd Law : T2 = KSR3 (with T: period, R: radius, and KS =

42

GM2E).

Potential: U = GM

Em

r , Total energy: E =GMm

2r GMm

r = GMm

2r .

Escape velocity: v =

2GM

R, Weightlessness:

mv2

R=

GMER2E

.

Forces: Weight W = mg

Friction Fk = k| N|eu (kinetic): eu direction of motion

Fs Fmaxs = s| N| (static): in direction opposite to applied force

Normal N force perpendicular to a surfaceTension T magnitude of the force propagated by a rope/string

Work and Work W = F D cos Energy: W = mg(yi yf) (gravity) , W = 12k(x

2f x

2i ) (spring)

Potential Energy U = mgh + C (gravity) , U = 12

kx2 + C (spring)Kinetic Energy K = 1

2mv2 (linear) , K = 1

2I2 (rotation)

Total Kinetic Energy: K = 12

mv2 + 12

I2

Work-energy theorem WNET = K = KfKiConservation of energy E = K+ UNon-conservative forces WNC = E = K+ U

Average Power P =W

t= Fv cos

Rotational angular quantities : s = R , v = R , a = R

motion: constant : = 0 + 0 t +1

2 t2, = 0 + t, 2 20 = 2( 0

UCM ( = 0) : = t and v =2R

Twhere T is the period and R the radius

Centripetal force : FR = maC = m2r =

mv2

raC: centripetal acceleration

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Physics 1501: Things to Know for the Final (contd)

Moment of inertia: I =Ni=1

mir2i and I = ICM + M R

2CM

ICM

= M R2 (ring), ICM

=1

2M R2 (disk), I

CM=

1

12M L2 (rod), I

CM=

2

5M R2 (sphere).

Torque and Torque = F r sin = Iangular momentum: Angular momentum L = I(using right-hand rule) Time variation = L/t

Conservation of angular momentum if EXT = 0 = Li = LfStatic equilibrium if

Fi = 0 and i = 0Oscillatory motion: Simple harmonic motion (T = 2/, and f = 1/T)

x = A cos(0t + ) , v =dx

dt= A sin(t + ) , a =

dv

dt= 2A cos(t + ) .

block-spring simple pendulum physical pendulum torsion pendulum

0 =

k

m0 =

g

L0 =

mgd

I0 =

I

Waves: General: y(x, t) = f(x vt).Superposition: y(x, t) = y1(x, t) + y2(x, t).Harmonic waves (1-D): y(x, t) = A cos(kx t + )

k

2

wave

number ,

2

T = 2f angular

frequency , v =

T =

k = f phase

velocity .

On a string: v =

T

velocity with T : tension

: mass per unit length

Fluids:

Pressure: P F/A = P0 + gh (fluid at rest).Pascals law: pressure applied to an uncompressible fluid is transmitted undiminished throughoutthe fluid and the walls on the container.Archimedes principle: FB = liquidV g (buoyant force).

Continuity equation: A1v1 = A2v2 = constant.Bernouillis equation: P +

1

2v2 + gh = constant.

Heat and temperature:

Thermal equilibrium: if objects in thermal contact have the same temperature.Thermal expansion: L = L0T (linear), and V = V0T (volume).Equation of state: P V = nRT (ideal gas).