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Centre of mass and rocket propulsion
- 1. CENTRE OF MASS & ROCKETPROPULSION MECHANICS & PROPERTIES OF MATTER GROUP VII1
- 2. CONTENT Centre of Mass What is Centre of Mass? Centre of Mass of symmetrical shape The Centre of Mass point for two mass system • 2D • 3D Rocket Propulsion 2
- 3. CENTRE OF MASS-(CM) •The location where all the mass of system could be concentrated to be located. • Make responses to the external forces and torques. • Distribution of mass is balanced around the CM. • Weighted average position coordinates defines the position. M1 M2 CM 3
- 4. CENTRE OF MASSOF SYMMETRICAL SHAPES 4
- 5. CM OF TWOIDENTICAL MASSES l l m m CM 5
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- 7. SOLID TRIANGLE PLATE x xx CM 7
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- 10. THE CENTRE OFMASS POINT FOR TWO-MASS SYSTEM 10
- 11. CM m1 m2 x x1 x2 Reference axis 𝑥= 𝑚1 𝑥1 + 𝑚2 𝑥2 𝑚1 + 𝑚2 11
- 12. If the systemis consist of “n” no. of mass particles, the position of the CM will be, 𝑥 = 𝑚1 𝑥1 + 𝑚2 𝑥2 + 𝑚3 𝑥3 + ⋯ + 𝑚𝑛𝑥𝑛 𝑚1 + 𝑚2 + 𝑚3 + ⋯ + 𝑚𝑛 𝑥 = Σ 𝑚𝑖𝑥𝑖 Σ𝑚𝑖 12
- 13. In the caseof a 3D system, Y Z X r1 rn R(n-1) R(n-2) r5 r4 r2 r3 m1 m5 m(n-1) m4 m3 m2 mn m(n-2) CM Position vector of CM is 𝑟 𝑟=x 𝑖+y 𝑗+z 𝑘 𝑥 = Σ𝑚𝑖 𝑥𝑖 𝑀 𝑦 = Σ𝑚𝑖 𝑦𝑖 𝑀 𝑧 = Σ𝑚𝑖 𝑧𝑖 𝑀 𝑟 = Σ𝑚𝑖 𝑀 {xi 𝑖+yi 𝑗+zi 𝑘} 𝑟 = 1 𝑀 Σ𝑚𝑖 𝑟𝑖 Where 𝑟𝑖 the position vector of 𝑖 𝑡ℎ mass of the system 13
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- 15. • Based onthe concept of “CONSERVATION OF MOMENTUM” V M at time “t” M V+Δ𝑉 Ve Δ𝑚 at time “t+Δt” 15
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