Phys 211 Formula Sheet - Course Websites · PDF filePhys 211 Formula Sheet Kinematics v = v0 +...
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Phys 211 Formula Sheet Kinematics v = v 0 + at r = r 0 + v 0 t + at 2 /2 v 2 = v 0 2 + 2a(x-x 0 ) g = 9.81 m/s 2 = 32.2 ft/s 2 v A,B = v A,C + v C,B Uniform Circular Motion a = v 2 /r = 2 r v = r = 2/T = 2f Dynamics F net = ma = dp/dt F A,B = -F B,A F = mg (near earth's surface) F 12 = -Gm 1 m 2 /r 2 (in general) (where G = 6.67x10 -11 Nm 2 /kg 2 ) F spring = - k x Friction f = k N (kinetic) f S N (static) Work & Kinetic energy W = Fdl W = Fr = F r cos (constant force) W grav = -mgy W spring = - k(x 2 2 - x 1 2 )/2 K = mv 2 /2 = p 2 /2m W NET = K Potential Energy U grav = mgy (near earth surface) U grav = -GMm/r (in general) U spring = kx 2 /2 E = K + U = W nc Power P = dW/dt P = Fv (for constant force) System of Particles R CM = m i r i / m i V CM = m i v i / m i A CM = m i a i / m i P = m i v i F EXT = MA CM = dP/dt Impulse I = F dt P = F av t Collisions: If F EXT = 0 in some direction, then P before = P after in this direction: m i v i (before) = m i v i (after) In addition, if the collision is elastic: *E before = E after * Rate of approach = Rate of recession * The speed of an object in the Center-of-Mass reference frame is unchanged by an elastic collision. Rotational kinematics s = R, v = R, a = R = 0 + 0 t + 1 / 2 t 2 = 0 + t = 0 2 + 2 Rotational Dynamics I = m i r i 2 I parallel = I CM + MD 2 I disk = I cylinder = 1 / 2 MR 2 I hoop = MR 2 I solid-sphere = 2 / 5 MR 2 I spherical shell = 2 / 3 MR 2 I rod-cm = 1 / 12 ML 2 I rod-end = 1 / 3 ML 2 = I (rotation about a fixed axis) r x F , rFsin Work & Energy K rotation = 1 / 2 I 2 , K translation = 1 / 2 MV cm 2 K total = K rotation + K translation W = Statics F = 0 , = 0 (about any axis) Angular Momentum: L = r x p L z = I z L tot = L CM + L * ext = dL/dt cm = dL * /dt precession = / L Simple Harmonic Motion: d 2 x/dt 2 = - 2 x (differential equation for SHM) x(t) = Acos( t + ) v(t) = -Asin( t + ) a(t) = - 2 Acos( t + ) 2 = k/m (mass on spring) 2 = g/L (simple pendulum) 2 = mgR CM /I (physical pendulum) 2 = /I (torsion pendulum) General harmonic transverse waves: y(x,t) = Acos(kx -t) k = 2/, = 2f = 2/T v = f = /k Waves on a string: length unit per mass tension F v 2 2 2 1 P A 2 v 2 2 A 2 1 dx E d 2 2 2 2 2 dt y d v 1 dx y d Wave Equation Fluids: m V F p A 11 2 2 Av Av 2 2 1 1 1 1 1 2 2 2 2 2 p v gy p v gy liquid liquid B gV F 1 2 1 2 A A F F Spring 2017
Transcript of Phys 211 Formula Sheet - Course Websites · PDF filePhys 211 Formula Sheet Kinematics v = v0 +...
Phys 211 Formula Sheet
Kinematics
v = v0 + at r = r0 + v0t + at2/2 v2 = v0
2 + 2a(x-x0)
g = 9.81 m/s2 = 32.2 ft/s2
vA,B = vA,C + vC,B
Uniform Circular Motion
a = v2/r = 2r v = r = 2/T = 2f
Dynamics
Fnet = ma = dp/dt FA,B = -FB,A
F = mg (near earth's surface) F12 = -Gm1m2/r2 (in general) (where G = 6.67x10-11 Nm2/kg2) Fspring = - k x
Friction
f = kN (kinetic) f SN (static)
Work & Kinetic energy
W = Fdl W = Fr = F r cos (constant force)
Wgrav = -mgy Wspring = - k(x2
2 - x12)/2
K = mv2/2 = p2/2m WNET = K
Potential Energy
Ugrav = mgy (near earth surface) Ugrav = -GMm/r (in general) Uspring = kx2/2 E = K + U = Wnc
Power
P = dW/dt P = Fv (for constant force)
System of Particles
RCM = miri / mi
VCM = mivi / mi ACM = miai / mi P = mivi
FEXT = MACM = dP/dt
Impulse
I = F dt P = Favt
Collisions:
If FEXT = 0 in some direction, then Pbefore = Pafter in this direction: mivi (before) = mivi (after)
In addition, if the collision is elastic: * Ebefore = Eafter* Rate of approach = Rate of
recession
* The speed of an object in
the Center-of-Mass reference
frame is unchanged by an
elastic collision.
Rotational kinematics
s = R, v = R, a = R = 0 + 0t + 1/2t2
= 0 + t = 0
2 + 2
Rotational Dynamics
I = miri2
Iparallel = ICM + MD2
Idisk = Icylinder = 1/2MR2 Ihoop = MR2 Isolid-sphere = 2/5MR2 Ispherical shell = 2/3MR2 Irod-cm = 1/12ML2 Irod-end = 1/3 ML2
= I(rotation about a fixedaxis)r x F , rFsin
Work & Energy
Krotation = 1/2I2 , Ktranslation = 1/2MVcm
2 Ktotal = Krotation + Ktranslation
W =
Statics
F = 0 , = 0 (about any axis)
Angular Momentum:
L = r x p Lz = IzLtot = LCM + L* ext = dL/dtcm = dL
*/dtprecession = / L
Simple Harmonic Motion:
d2x/dt2 = -2x (differential equation for SHM)
x(t) = Acos(t + ) v(t) = -Asin(t + ) a(t) = -2Acos(t + )
2 = k/m (mass on spring)
2 = g/L (simple pendulum)
2 = mgRCM/I (physical pendulum)
2 = /I (torsion pendulum)
General harmonic transverse waves:
y(x,t) = Acos(kx -t) k = 2/, = 2f = 2/T v = f = /k
Waves on a string:
lengthunit per mass
tensionFv2
2 21P A2
v
22A21
dxEd
2
2
22
2
dtyd
v1
dxyd Wave Equation
Fluids:
m
V
Fp
A
1 1 2 2Av A v
2 21 11 1 1 2 2 22 2p v gy p v gy
liquidliquidB gVF
1
212
A
AFF
Spring 2017
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