Physics: Motion, Laws, Work, Energy, Gravitation

Motion in a Straight Line

V=u+at[V-T relation] (a=slope=∆x/∆ y=v-u/t)

S=ut+1/2at² [Position-T relation](displacement=area under V-T Graph=Area of rectangle+area of triangle)

v² =u² +2as[Position-velocity relation](displacement=area of trapezium=[a+b/2]h

S=v² -u² /2a

stopping distance: S=-u² /2a

Motion In a Plane

cosθ =Ax/A

sinθ =Ay/A

tanθ = Ay/Ax

| sin²θ+cos²θ=1|

magnitude of a vector; A= √Ax² +Ay²+Az² = √ Ax² +Ay²

substraction of vectors: A-B = A+(-B)

//logram law of vector addition :- [R=A+B][PN=Bcosθ][SN=Bsinθ] [R=√vb²+vc²+2VbVcCosθ

Time of flight:T=2usinθ/g→Full motion [uSinθ/g→half]

Max height: H=u²sinθ/2g

horizontal range:R=u²sin2θ/g [sin2θ =2sSnθCosθ]

Angular velocity/speed : ω(angular V) = ∆θ/∆t

linear velocity: V=rω or V=ωR

angular acceleration(ac): a=(v²/r)=(v²/R→is radius)=(ω²R)=(Vω)

tanθ=sinθ/cosθ or θ=tan-¹sinθ/cosθ

Laws of Motion

Newton's 1st law(inertia):Every body continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to change that state.

2nd law:The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts. (F=∆p/∆t)

3rd law:To every action, there is always an equal and opposite reaction.

Impulse = Force × time duration (Fxt)(I = dp→Impulse = change in momentum )(momentum=mv)

[R=mg→when it is at rest or constant v][R=m(g+a) when lift is ↑][m(g-a) ↓]

law of conservation momentum:he total momentum of an isolated system of interacting particles is conserved.

Static friction:( 𝐟𝐬 )𝐦𝐚𝐱 = 𝛍𝐬𝐍or fs ≤ 𝛍𝐬N & a max = 𝛍𝐬g

𝛍 𝐬(coefficient of static friction) = 𝐭𝐚𝐧θ(Q.what is the coefficient of static friction b/w ) θ = 𝐭𝐚𝐧−𝟏 𝛍𝐬

(Motion of a vehicle on a curved level road)𝐯² ≤ 𝛍𝐬𝐑𝐠 & 𝐯𝐦𝐚𝐱 = √𝛍𝐬𝐑𝐠 [R=radius of the road]

(optimum speed)𝐯𝐨𝐩𝐭𝐢𝐦𝐮𝐦= √𝐑𝐠 𝐭𝐚𝐧 𝛉 [R=radius,g=gravity,tanθ=is angle of banked road] [banked road]

𝐯𝐦𝐚𝐱 = √ 𝐑𝐠(𝛍𝐬+𝐭𝐚𝐧 𝛉 )/𝟏 −𝛍𝐬 𝐭𝐚𝐧 θ [ vehicle on a banked road]

Work Energy and Power

𝐀⃗ ⋅ 𝐁⃗ = 𝐀𝐁 𝐜𝐨𝐬𝛉

cosθ = vector F . vector d/ d.f

F =√Fx 2 + Fy 2 + Fz 2

vectorf x vector d = fxdx=fydy=fzdz

W = F d cos θ (how much work does the non moving thing does on moving thing) & W = 𝐅⃗ ⋅ 𝐝→

Kinetic energy: K = ½ 𝐦𝐯̅ ⋅ 𝐯̅ = ½ 𝐦𝐯²

Hooks law:Hooke’s law states that ,for an ideal spring, the spring force F is proportional displacement x of the block from the equilibrium position.

power:P= F . v

F = m g + Frictional Force

to covert to watt power to horsepower divide it by 746

Centre Of Mass 𝐑⃗ = 𝐦𝟏 vector r𝟏+𝐦𝟐 vect𝐫𝟐/ 𝐌 [where M=𝒎𝟏 + 𝒎𝟐]

torque: = vector r x vect f

Gravitation

Kepler’s Laws: 1.Law of orbits All planets move in elliptical orbits with the Sun situated at one of the foci of the ellipse.

2.Law of areas The line that joins any planet to the sun sweeps equal areas in equal intervals of time. i.e, 𝐚𝐫𝐞𝐚𝐥 𝐯𝐞𝐥𝐨𝐜𝐢𝐭𝐲 𝚫𝐀⃗ /𝚫𝐭 is 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭

3.Law of periods The square of the time period of revolution of a planet is proportional to the cube of the semi- major axis of the ellipse traced out by the planet. 𝐓²∝ 𝐚³

force : 𝐅 = 𝐆 𝐦𝟏𝐦𝟐 𝐫 𝟐

g= 𝐆𝐌/𝐑². Gravitational constant: G = 6.67×1𝟎 raise to −𝟏𝟏 N 𝐦² /𝐤𝐠²

gh = g(1 + h/R )-² (Acceleration due to gravity at a height h above the surface of the earth.)

g𝐝 = 𝐠(𝟏 − 𝐝/𝐑 )Acceleration due to gravity at a depth d below the surface of the earth