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For mul a Bookl et Physi cs XI
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Formula Booklet – Physics XI
CONTENTS Description
Page Number
1.
Units, Dimensions & Measurements
03
2.
Motion in one Dimension & Newton’s Laws of Motion
04
3.
Vectors
06
4.
Circular Mo Motion, Relative Motion, and Projectile Motion
07
5.
Friction & Dynamics of Rigid Body
09
6.
Conservat ion Laws & Collisions
12
7.
Simple Harmonic Motion & Lissajous Figures
14
8.
Gravitation
18
9.
Propertie s of Matter
20
10. Heat & Thermodynamics
25
11. Waves
30
12. Study Tips
35
2
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Formula Booklet – Physics XI
UNITS,DIMENSIONSANDMEASUREMENTS (i)
SI Un Units: (a) (a) Time Time-s -sec econ ond( d(s) s);; (b) (b) Leng Length th-m -met etre re (m); (m); (c) (c) Mass Mass-k -kil ilog ogra ram m(k (kg) g);; (d) Amountof Amountofsu substa bstance– nce–mole mole(mo (mol); l);(e) (e)Temp Temperat eratureure-Kelvi Kelvin( n(K); K); (f) Electr Electric icCur Curren rent– t–a ampe mpere re(A) (A);; (g) Lumin Luminous ousI Inte ntensi nsity ty–C –Can andel dela a(Cd (Cd))
(ii)
Usesof Usesofdimen dimensio sionala nalanaly nalysis sis
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Formula Booklet – Physics XI
CONTENTS Description
Page Number
1.
Units, Dimensions & Measurements
03
2.
Motion in one Dimension & Newton’s Laws of Motion
04
3.
Vectors
06
4.
Circular Mo Motion, Relative Motion, and Projectile Motion
07
5.
Friction & Dynamics of Rigid Body
09
6.
Conservat ion Laws & Collisions
12
7.
Simple Harmonic Motion & Lissajous Figures
14
8.
Gravitation
18
9.
Propertie s of Matter
20
10. Heat & Thermodynamics
25
11. Waves
30
12. Study Tips
35
2
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Formula Booklet – Physics XI
UNITS,DIMENSIONSANDMEASUREMENTS (i)
SI Un Units: (a) (a) Time Time-s -sec econ ond( d(s) s);; (b) (b) Leng Length th-m -met etre re (m); (m); (c) (c) Mass Mass-k -kil ilog ogra ram m(k (kg) g);; (d) Amountof Amountofsu substa bstance– nce–mole mole(mo (mol); l);(e) (e)Temp Temperat eratureure-Kelvi Kelvin( n(K); K); (f) Electr Electric icCur Curren rent– t–a ampe mpere re(A) (A);; (g) Lumin Luminous ousI Inte ntensi nsity ty–C –Can andel dela a(Cd (Cd))
(ii)
Usesof Usesofdimen dimensio sionala nalanaly nalysis sis
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For mul a Bookl et Physi cs XI (a) (b) (c)
Tocheck Tocheckthe theac accura curacy cyofa ofagiv given enrela relation tion Toderiv Toderivea earelat relative ivebetw between eendiffe different rentphys physical icalqua quantiti ntities es Toconve Toconverta rtaphy physica sicalqu lquantit antityf yfromo romones nesyste ystemto mtoano another thersyst system em a
n1u 2 = n 2 u 2
b
M1 L1 T1 x x M L 2 2 T2
c
n 2 = n1
or
X1 − X 2 + ... + XN
(iii) Meanor Meanoraver average agevalu value e: X =
N
(iv) Absolute Absoluteerror errorin inea eachme chmeasur asuremen ementt :|∆Xi|=| X–Xi| (v)
Meana Meanabs bsolu olute teerr error or: ∆Xm=
Σ | ∆ Xi | N
∆X X ∆X (vii) Percentag Percentagee eerror rror= = x 100 X
(vi) (vi) Fracti Fractiona onal lerr error or= =
X a Yb
(viii) Combinationofer Combinationoferror ror:If :Ifƒ = ∆ƒ
∆X
∆Y
Zc
,thenmaximumfractionalerrorin
ƒ is:
∆Ζ
ƒ =| a | X + |b | Y + | c | Ζ
3
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Formula Booklet – Physics XI
MOTIONINONEDIMENSION&NEWTON’SLAWSOFMOTION
Displacement:|displacement| Displacement:|displacement| ≤ distancecovered Averagespeed : v =
(a)
s1 + s 2 t1 + t 2
s1 + s 2 s1 s 2 + v1 v 2
=
2v v
1 2 Trying to print this document? If s1 =s =Harmonicmean 2 =d,then v =
v1 + v 2
of 35
v +v
1 printing 2 Scribd documents from your browser doesn't work well. Instead, we recommend you download this document as a If t 1 =tUnfortunately, =arithmeticmean 2,then v =
Readcast
(b)
Not Readcasted(iii)
Averagevelocity :(a) v av =
2 PDF file and use your PDF reader to print. →
→ → r2 − r1
Download and Print t 2 − t1 →
→
;(b) | v av | ≤ v
→
→
d Note: You can alway always clInstantaneousvelocity ick on the the Readcast Readcast button button shrare with wi you r Scribd Scribd fol follo lowers. wers. (iv)s cli : vto =v=instantaneousspeed = share and | th v | your
Auto-Readcasting: OffView Past Readcasts (v) Averageacceleration : Undo (vi) Add a comment Submit
(vii)
→ a av =
dt → → v 2 − v1
2 t→ − t1 →
Instantaneousacceleration : a = d v / dt dv Inone–dimension,a=(dv/dt)= v dx Equationsofmotioninonedimension : (a) (a) v= u+ u+at at;;
Auto-Readcasting: OffView Past Readcasts 1 2 Like
40
Tweet
(b)
x = ut +
at ;
(c)
v 2 u2 +2ax;
(d)
x = vt –
2 1 2
2
at ;
v + u
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Formula Booklet Physics XI 2 1
at 2 ;
(f)
s = x − x 0 = ut +
(g)
v =u +2a(x–x 0)
2
2
2
a
(viii) Distancetravelledinnthsecond :dn =u+
2
(2n–1)
2
(ix)
Motionofaball : (a)whenthrownup:h=(u /2g) andt=(u/g) (b)whendropped:v= √ (2gh) and t= √(2h/g)
(x)
Resultantforce :F= √(F1 +F2 +2F 1F2 cos θ)
(xi)
Conditionforequilibrium :(a) F3 = − (F1 + F2 ) ; (b)F1 +F2 ≥ F3 ≥ |F1 –F2|
(xii)
Lami’sTheorem :
(xiii)
2
2
→
→
→
P Q R = = sin (π − α ) sin (π − β) sin (π − γ) → → → → Newton’ssecondlaw : F = m a ; F = dp / dt
Search This Document
→ → Search 2 (xiv) Impulse: ∆p = F ∆t and p 2 −p1 = ∫ 1 Fdt Search History: (xv) Newton’sthirdlaw : Searching... Result 00 of 00 QUEST-PowerCoachingforIITJEE 00 results for result for 1,VigyanVihar,NearAnandVihar,Delhi–92.Ph:55270275,55278916 p. E-16/289,Sector8,Rohini,Delhi–85,Ph:55395439,30911585
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4
Formula Booklet – Physics XI
(1)
(a)
→ → F12 = − F12
(b)
Contactforce: F12 =
(c)
M m
(2)
F = F21
M+m F Acceleration:a= M+m
F
F21 Fig.1
(xvi) Inertialmass :mI =F/a (xvii) Gravitationalmass :mG =
F12
m
F g
=
FR2 GM
; m I = mG
→
(xviii) Noninertialframe :If a 0 betheaccelerationofframe,thenpseudoforce Example:Centrifugalforce=
mv
2
→ → F = −m a 0
= m ω2 r
r
(xix) Liftproblems :Apparentweight=M(g ± a0) (+signisusedwhenliftismovingupwhile–signwhenliftismovingdown) m1
(xx)
T
PulleyProblems: (a) Forfigure(2): Tensioninthestring,T=
m1m 2 m1 + m 2
Frictionless surface
g
m2
m2
Accelerationofthesystem,a=
g
m1 + m 2
Theforceonthepulley,F= (b)
2 m1 m 2 m1 + m 2
T
Fig.2
m2g
g
Forfigure(3): Tensioninthestring, T =
2m1m 2 m1 + m 2
Accelerationofthesystem, a =
Theforceonthepulley, F =
g
a
m 2 − m1 m 2 + m1
4m1m 2 m1 + m 2
•
T T
g
g
T T a
m1 Fig.3
m2
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Formula Booklet – Physics XI
VECTORS →
→
→
→
→
→ →
→
→
(i)
Vectoraddition : R = A + B = B + A and A − B = A+ (− B )
(ii)
Unitvector: A = ( A/ A)
(iii)
Magnitude: A = √ (A 2x + A 2y + A 2z )
(iv)
Directioncosines :cos α =(Ax/A),cos β =(Ay/A),cos γ=(Az/A)
(v)
Projection:
→
^
→
(vi)
→ ^
Componentof A along B = A . B
(b)
Component
(c)
If A = A x i + A y j, thenitsanglewiththex–axisis
→
→
→
^
→
of B along A = A . B
^
^
θ =tan–1 (Ay/Ax)
Dotproduct : → → A . B =ABcos θ,
(a) (vii)
→
(a)
→ → A . B = A xBx
(b)
+ A y B y + A z Bz
Crossproduct : ^ n
→ → A x B = ABsin → → A x A = 0;
θ
(a) (b)
→
(c)
→
Ax B=
;
^
^
^
i
j
k
Ax
Ay
Az
Bx
By
Bz
(viii) Examples: W= → F .→ r;
(a) →
→
→
(e) v = w x r ;
(b) P = → F .→ v; →
→
→; (c) φ Ε = → E .A
→ → → (g) F m = q v x B
→
(f) τ = τ x F ;
→
→
(ix)
Areaofaparallelogram :Area= | A x B |
(x)
Areaofatriangle :Area=
(xi)
Gradientoperator: V = i
(xii)
→ → → Volumeofaparallelopiped : V = A . B x C
^
(d) φΒ = → B .→ A;
1 → → |Ax B| 2
∂ ^ ∂ ^ ∂ + j + k ∂x ∂y ∂z
6
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Formula Booklet – Physics XI
CIRCULARMOTION,RELATIVEMOTION&PROJECTILEMOTION (i)
UniformCircularMotion : (a) v = ωr; 2 2 (b) a = (v /r)= ω r; 2 (c) F = (mv /r); (d) (e)
(ii) iii
→ → r . v = 0; → → v.a =0 2
Cyclisttakingaturn :tan θ =(v /rg) Cartakin aturnonlevelroad :v= √
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Formula Booklet Physics XI 2
(iv)
BankingofRoads :tan θ =v /rg
(v)
Airplanetakingaturn :tan θ =v /rg
(vi)
Overloadedtruck : (a) Rinner wheel <Routerwheel (b) maximumsafevelocityonturn,v= √(gdr/2h)
(vii)
Non–uniformCircularMotion : 2 (a) Centripetalaccelerationa r =(v /r); (b) Tangentialaccelerationa t =(dv/dt); (c) Resultantaccelerationa= √ (a 2r + a 2t )
2
(viii) MotioninaverticalCircle : 2 2 (a) ForlowestpointAandhighestpointB,T A –TB =6mg;v A =v B +4gl ;vA ≥ √(5gl);andv B≥ √ (gl) (b) ConditionforOscillation:v A < √(2gl) (c) ConditionforleavingCircularpath: √(2gl)<vA < √(5gl) →
→
→
(ix)
Relativevelocity : v BA = v B − v A
(x)
ConditionforCollisionofships : ( r A − v B ) x ( v A − v B ) = 0
(xi)
CrossingaRiver: (a) BeatKeepsitsdirectionperpendiculartowatercurrent –1 (1) v R =√( (v 2w + vb2 ) ; (2) θ =tan (v w / vb );
→
(3) (b)
→
→
→
t=(x/v b)(itisminimum) (4) Driftonoppositebank=(v w/vb)x Boattoreachdirectlyoppositetostartingpoint: (1)sin θ =(vw/vb); (2)v resultant =vb cos θ ; (3)t=
(xii)
x vb cos θ
Projectilethrownfromtheground : gx
2
(a)
equationoftrajectory:y=xtan θ –
(b)
timeofflight: T =
(c) (d)
Horizontalrange,R=(u sin2 θ/g) 2 2 Maximumheightattained,H=(u sin θ/2g)
2
2
2u cos θ
2 u sin θ g 2
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