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PHYSICS FORMULA SHEET KINEMATICS Linear

v =v O + at 2 2 v f =v O +2 a ∆ x 1 ∆ x=v O t+ a t 2 2

ECE

W =Fdcosθ =madcosθ 1 2 KE(translational)= m v 2 W = Δ KE(work −energy theorem) PE=mgh W = Δ KE( translational) + Δ PE

Free fall

v y =v Oy −¿ v 2fy=v2Oy−2 g ∆ y 1 2 ∆ y=v Oy t− g t 2 Projectile Motion

v OX =v O cosθ v Oy =v O sinθ range = vO cosθ (t total) v fy=v O sinθ−¿ v o sinθ t(half flight)= g 2 v o sinθ t (full flight )= g 2 ( v o sinθ ) y max = 2g

Conservation of Energy Theorem

Δ KE(Translational )+ Δ PE=0 w P= t IMPULSE, MOMENTUM, AND COLLISION

J (impulse )=F Δt=∆ P P(momentum)=mv Law of Conservation of Momentum

m 1 v 1+ m2 v 2=m1 u1+ m 2 u2 u2−u1 e(coefficient of resitution)= v 1−v 2 Perfectly Inelastic Collision

m 1 v 1+ m2 v 2= ( m1 +m 2 ) u e=0

NEWTON’S LAW OF MOTION ROTATIONAL KINEMATICS Law of acceleration

∑ F=ma

1st condition of Equilibrium

∑ F x =0∧∑ F y =0 f (frictional force ) =μ F n

s=rθ v =rω a(tangential)=r α Total Magnitude of Acceleration 2 2 a= √ a(tangential ) +a(centripetal)

v2(tangential) r 2 a( centripetal)=ω r 1 T ( period )= f ω=2 πf 2 2π 2 4π r 2 r= 2 a( centripetal)=ω r= t T a(centripetal)=

( )

TORQUE and MOMENT OF INERTIA

τ =Frsinθ 2 I ( point mass)=m r τ =Iα 1 2 I ( solid cylinder−center) = mr 2 2 I (sphere −center) = mr 2 5 1 2 I (rod−center )= m l 12 1 2 I (cylinder−diameter )= ml 12 1 2 I (rod−end )= ml 3 ANGULAR MOMENTUM, ROTATIONAL ENERGY and POWER

l=rp=rm v (tangential) l=Iω 1 KE(rotational)= I ω 2 2 P=τω I 1 ω1 =I 2 ω2 W =τθ

FLUID MECHANICS

m V mg =ρg D (weight density)= V ρ substance D substance specific gravity= = ρ fluid D fluid w object=wliquid displaced V fluid displaced =V submerged F B=V fluid displaced=m f =ρ f V f g= ρf V ( submerg weight app=weight −F b F P= A Po (atmospheric pressure)=ρgh P A ( absolute pressure) =P o + PG A 1 V 1= A 2 V 2(continuity equation) ρ(mass density)=

Pascals Principle

P1=P2 F1 F 2 = A 1 A2

Bernoulli’s Equation

P1+ ρg y 1 +

1 2 1 2 ρ v =P 2+ ρg y 2 + ρ v 2 2 1 2

Torrichelli’s Theorem

u2= √2 gh

WORK, ENERGY, AND POWER

KASMacaraeg January 2019

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