Centre Of Mass Short Notes PDF

# Short Notes- - What mass assume to be conc. - *Ki on intersection of Aos - Kcom = m1*r1 + m2*r2 / m1+m2 - Vcom = m1*v1 + m2*v2 / m1+m2 - *acm = m1*a1 + m2*a2 / m1+m2 # Position depends on choice of origin #2 Rem from any one mass - (xcm)1 = m2*R / m1+m2 - (xcm)2 = m1*R / m1+m2 #3 Vimp. Moment...

# Short Notes- - What mass assume to be conc. - *Ki on intersection of Aos - Kcom = m1*r1 + m2*r2 / m1+m2 - Vcom = m1*v1 + m2*v2 / m1+m2 - *acm = m1*a1 + m2*a2 / m1+m2 # Position depends on choice of origin #2 Rem from any one mass - (xcm)1 = m2*R / m1+m2 - (xcm)2 = m1*R / m1+m2 #3 Vimp. Moment of mass - Com wo point jisko along 2 body ka momentof mass equal nata h #4 Continuous mass system - *xcm = ∫ x dm / ∫ dm - dm *fdm -> Rod [1D] - dm ** oda -> Square, Wing [2D] - dm * Idv -> Sphere [3D] #5 Com of Special bodies - Rod: 4/2 - Hay Disc: 4R/3π - Half Ring: 2R/π - **Hollow Hemisphrere: 4R/8 - Hollow core: h/3 - Solid core: h/4 - Pot Hemisphrere: 4πR/8 #6 Cavity wall ques- - Cavity aur remaining ka moment of mass centri h along equal kar dena #2 Shift in Pos of com - *d*r*cm = m1*d*r1 + m2*d*r2 / m1+m2 - For No movement of com - m1*d*r1 = -m2*d*r2 #8 acm in Pulley Block System - acm = -(m2-m1)^2 / (m1+m2)*g #9 Momentum - For a body: F = dP / dt - : If Fem = 0 Pcm = Const - Vcm = Const - acm = 0 - Vcom = 0 [may be] - If V com = 0 - For System: Fext = dPcm / dt # Internal forces - Since com no koi farak nahi - But KE change hog? #10 Explosion - - M - Fext=0 - Pcm = Const - (sys) - 1/2 * mV^2f + 1/2 * mV^2i - Q = Kf - Ki = 1/2 * mv^2f + 1/2 * mV^2i - Energy release in Explosion #11 Collision * - e = separation / muom - = (V1-V2) / (U2-U1) #12 Elastic Collision - KEi = KEf - Pi = Pf - V1 = (m1-m2/m1+m2) * U1 + 2m2/m1+m2 * U2 - ΔKE = 0 # Special loses! - (m1 + m2) v = m - Vel interchange hojayegi #13 Inelastic Collisions - Pi = Pf - KGi ≠ KEf - V1 = (m1-m2/m1+m2) * U1 + b*U2 (m1+m2/m1+m2) - ΔNE =~ 1/2 * mm / m1+m2 * (V^2i - V^2f) #14 Perfectly Inelastic < - Pi = Pf - Brick to Each Other - KCi ≠ KEf - Vο comunes = m1*U1 + m2 *U2/ m1+m2 - ANE = 1/2 * m1 * m2 /m1+m2 *(V0)^2 #15 Inelastic Collision - Blue Ball & Ground - V^2f = √2ghBc - Sm =L hBc - L = √hAc/hBc #16 Oblique Collision - 1 * on * every ≠ omnis pe khel - 2 * P= Conserved kar de - 3 * Agar Plastic h to KEi = KEf kar de - 4 And Phoddi quy-ka.