Physics Crib Sheet
Physics Crib Sheet Mo#on in One Dimension Vx,avg=
∆x
d
Average Velocity
∆t
Vavg= ∆t
Posi8on as func8on Of 8me
xf= xi + vxt
∆vx ax,avg= ∆t
Force propor8onal vxf= vxi + axt to accelera8on
Fx ∝ ax
Pos. as func8on of vel. & 8me
xf= xi + ½(vxi+vxf)t
Average Speed
xf= xi + vxit + ½axt2
Average Accel
velocity as func8on Of 8me
Pos. as func8on of 8me, accel.
Mo#on in Two Dimensions rf= ri + vit + ½gt2
Posi8on vector as func8on of 8me
vi2 sin2ϴi R = g
Range
Centripetal Accelera8on
v2 ac= r
2πr T= v
vi sinϴi t = g
Time at which projec8le reaches peak
vi2 sin2ϴi h = 2g
Max Height
Period of Circular Mo8on
4π2r ac= T2
Centripetal Accelera8on
The Laws of Mo#on 1. When viewed from an iner8al frame, an object at rest remains at rest & an object in mo8on remains in mo8on 2. When viewed from an iner8al frame, the accelera8on of an object is directly propor8onal to net force ac8ng on it and inversely propor8onal to its mass. (F= ma) ∴ (Fg= mg) 3. If two objects interact, the force F12 exerted by the object 1 on object 2 is equal in magnitude and opposite in direc8on to the force F21 exerted by object 2 on object 1. (F12 = -‐F21)
Force of Fric8on
Ff=μfn
Tanϴ=μ
μSta8c fric8on > μKine8c fric8on
Circular Mo#on 2 ∑F= mac= m vr
vmax= √μsgr
Net force causing centripetal accelera8on
v2 Tanϴ= rg
Max speed around curve
Resis#ve Forces R= -‐bv Resis8ve force ac8ng on object Drag ~ v
Angle of Banked Curve
Liquids
Drag ~ v2
vT= mg b Low Density Fluids
Terminal Speed Through resistance • hcosϴ finds adjacent vector • hsinϴ finds opposite vector
Energy W=F*d
Work KE= ½ mv2
Kine8c Energy W= ½ kx2
Work Done PE= mgh By Spring
Poten8al Energy
Linear Momentum & Collisions Momentum
P= mv
Impulse
I= Favg * ∆t = ∆p
∆p = mvf -‐ mvi
Impulse
Mo8on of a Velocity system of par8cle Vf= √vi2+2(h-‐y) from change about cm in height Inelas8c Collision Elas8c Collision in m1v1i + m2v2i = (m1+m2)vf v1i – v2i = v2f – v1f in One Dimension One Dimension 2m2 m1-‐m2 m2-‐m1 2m1 One D vif = m +m v1i + m +m v2i v2f = m vf – vi = ve ln(mi/mf) Rocket +m v1i + m +m v2i 1 2 1 2 Propulsion 1 2 Results 1 2 Rota#ons of a Rigid Object Change in Change in Change 2 2 2 Angular Angular Θ = Θo + ωt + ½ αt ω = ωo + αt ω = ωo + 2αΘ in angle Velocity Velocity Θ = ½ (ω + ωo)t Elas8c Collision in Ma = ∑F cm i One Dimension
∆vi= -‐∆vf
Tangen8al Linear at = αr velocity
v = ωr
Radial Accelera8on
ar = ω2r τ= r*F
Tangen8al atotal = √(r2α2 + r2ω2) Linear accelera8on
torque τ= rFsinθ
torque τ= Iα
Moments of Iner8a Hoops: MR2
Solid Cylinder: ½ MR2
Hollow Cylinder: 1/2M(R12-‐R22)
Angular Momentum L= Ioωo Gravita#on U(r)= -‐GMm r
x(t)= Acos(ωt+φo)
Ipa= Icm + MD2
RodEnd: 1/3ML2
Rectangular Plate: 1/12M(a2+b2)
Angular Momentum conserved
L= r x p
Parallel Axis Theorem Power of torque
Work done P=τω by torque
torque W= τΘ
Rodcentre: 1/12ML2
Gravita8onal 2 T2= 4π r3 Poten8al GM Energy
Oscillatory Mo#on
Iner8a of Pointmass
Ipointmass= mr2
Rota8onal Kine8c Energy
Linear K = ½ Iω2 accelera8on tot
Solid Sphere: 2/5MR2
Spherical Shell: 2/3MR2
Angular Momentum in Linear Mo8on
Planetary Mo8on Etotal= -‐GMm 2r (Kepler’s)
Sinusoidal displacement A-‐amplitude, φ-‐ loca8on of mass @ t=0, ω= natural frequency
Energy in Orbital vescape= √2GM r Mo8on Universal Gravita8on Constant: 6.67x10-‐11Nm2/kg
v(t)= -‐ωAsin(ωt+φo)
a(t)= -‐ωA2cos(ωt+φo)
Hooke’s Mass on Pendulum F= -‐kA Period f= 1 ω=√(g/L) frequency ω=√(k/m) Law spring T Waves & Sound (Longitudinal Wave) Shape of wave Speed of Speed of Speed of y(x,t)= Asin(kx-‐ωt+φo) k= 2π/λ v= fλ ω= 2π/T func8on wave wave wave Speed of wave Power of Energy of Beat 2 2 P= ½ μω2A2v v= √(T/μ) f = a bs(f -‐ f (string) μ= mass/ Eλ= ½ μω A λ beat 1 2 wave wave freq. length Frequency of open air Frequency of Beats fn= n(v/2L) fn= n(v/4L) β= 10log(I/Io) column (& string wave) closed air column T= 2π ω
v_____ sound ± vobs f’= f( v sound ± v source )
1_____ +/-‐ if source & observer f’= f ( /v sound ) 1 ± vsource moving toward eachother
If source moves toward (-‐) or away (+) from observer
∆x
d
Average Velocity
∆t
Vavg= ∆t
Posi8on as func8on Of 8me
xf= xi + vxt
∆vx ax,avg= ∆t
Force propor8onal vxf= vxi + axt to accelera8on
Fx ∝ ax
Pos. as func8on of vel. & 8me
xf= xi + ½(vxi+vxf)t
Average Speed
xf= xi + vxit + ½axt2
Average Accel
velocity as func8on Of 8me
Pos. as func8on of 8me, accel.
Mo#on in Two Dimensions rf= ri + vit + ½gt2
Posi8on vector as func8on of 8me
vi2 sin2ϴi R = g
Range
Centripetal Accelera8on
v2 ac= r
2πr T= v
vi sinϴi t = g
Time at which projec8le reaches peak
vi2 sin2ϴi h = 2g
Max Height
Period of Circular Mo8on
4π2r ac= T2
Centripetal Accelera8on
The Laws of Mo#on 1. When viewed from an iner8al frame, an object at rest remains at rest & an object in mo8on remains in mo8on 2. When viewed from an iner8al frame, the accelera8on of an object is directly propor8onal to net force ac8ng on it and inversely propor8onal to its mass. (F= ma) ∴ (Fg= mg) 3. If two objects interact, the force F12 exerted by the object 1 on object 2 is equal in magnitude and opposite in direc8on to the force F21 exerted by object 2 on object 1. (F12 = -‐F21)
Force of Fric8on
Ff=μfn
Tanϴ=μ
μSta8c fric8on > μKine8c fric8on
Circular Mo#on 2 ∑F= mac= m vr
vmax= √μsgr
Net force causing centripetal accelera8on
v2 Tanϴ= rg
Max speed around curve
Resis#ve Forces R= -‐bv Resis8ve force ac8ng on object Drag ~ v
Angle of Banked Curve
Liquids
Drag ~ v2
vT= mg b Low Density Fluids
Terminal Speed Through resistance • hcosϴ finds adjacent vector • hsinϴ finds opposite vector
Energy W=F*d
Work KE= ½ mv2
Kine8c Energy W= ½ kx2
Work Done PE= mgh By Spring
Poten8al Energy
Linear Momentum & Collisions Momentum
P= mv
Impulse
I= Favg * ∆t = ∆p
∆p = mvf -‐ mvi
Impulse
Mo8on of a Velocity system of par8cle Vf= √vi2+2(h-‐y) from change about cm in height Inelas8c Collision Elas8c Collision in m1v1i + m2v2i = (m1+m2)vf v1i – v2i = v2f – v1f in One Dimension One Dimension 2m2 m1-‐m2 m2-‐m1 2m1 One D vif = m +m v1i + m +m v2i v2f = m vf – vi = ve ln(mi/mf) Rocket +m v1i + m +m v2i 1 2 1 2 Propulsion 1 2 Results 1 2 Rota#ons of a Rigid Object Change in Change in Change 2 2 2 Angular Angular Θ = Θo + ωt + ½ αt ω = ωo + αt ω = ωo + 2αΘ in angle Velocity Velocity Θ = ½ (ω + ωo)t Elas8c Collision in Ma = ∑F cm i One Dimension
∆vi= -‐∆vf
Tangen8al Linear at = αr velocity
v = ωr
Radial Accelera8on
ar = ω2r τ= r*F
Tangen8al atotal = √(r2α2 + r2ω2) Linear accelera8on
torque τ= rFsinθ
torque τ= Iα
Moments of Iner8a Hoops: MR2
Solid Cylinder: ½ MR2
Hollow Cylinder: 1/2M(R12-‐R22)
Angular Momentum L= Ioωo Gravita#on U(r)= -‐GMm r
x(t)= Acos(ωt+φo)
Ipa= Icm + MD2
RodEnd: 1/3ML2
Rectangular Plate: 1/12M(a2+b2)
Angular Momentum conserved
L= r x p
Parallel Axis Theorem Power of torque
Work done P=τω by torque
torque W= τΘ
Rodcentre: 1/12ML2
Gravita8onal 2 T2= 4π r3 Poten8al GM Energy
Oscillatory Mo#on
Iner8a of Pointmass
Ipointmass= mr2
Rota8onal Kine8c Energy
Linear K = ½ Iω2 accelera8on tot
Solid Sphere: 2/5MR2
Spherical Shell: 2/3MR2
Angular Momentum in Linear Mo8on
Planetary Mo8on Etotal= -‐GMm 2r (Kepler’s)
Sinusoidal displacement A-‐amplitude, φ-‐ loca8on of mass @ t=0, ω= natural frequency
Energy in Orbital vescape= √2GM r Mo8on Universal Gravita8on Constant: 6.67x10-‐11Nm2/kg
v(t)= -‐ωAsin(ωt+φo)
a(t)= -‐ωA2cos(ωt+φo)
Hooke’s Mass on Pendulum F= -‐kA Period f= 1 ω=√(g/L) frequency ω=√(k/m) Law spring T Waves & Sound (Longitudinal Wave) Shape of wave Speed of Speed of Speed of y(x,t)= Asin(kx-‐ωt+φo) k= 2π/λ v= fλ ω= 2π/T func8on wave wave wave Speed of wave Power of Energy of Beat 2 2 P= ½ μω2A2v v= √(T/μ) f = a bs(f -‐ f (string) μ= mass/ Eλ= ½ μω A λ beat 1 2 wave wave freq. length Frequency of open air Frequency of Beats fn= n(v/2L) fn= n(v/4L) β= 10log(I/Io) column (& string wave) closed air column T= 2π ω
v_____ sound ± vobs f’= f( v sound ± v source )
1_____ +/-‐ if source & observer f’= f ( /v sound ) 1 ± vsource moving toward eachother
If source moves toward (-‐) or away (+) from observer
