Vγ⋅dP+P⋅γVγ−1⋅dV=0cap V raised to the gamma power center dot d cap P plus cap P center dot gamma cap V raised to the gamma minus 1 power center dot d cap V equals 0
τ⃗=r⃗×F⃗modified tau with right arrow above equals modified r with right arrow above cross modified cap F with right arrow above Expanding the cross product via determinant:
Let a projectile be launched with velocity at an angle to the horizontal.Horizontal component: , Vertical component: .Horizontal distance at time
R=(ucosθ)⋅T=(ucosθ)⋅(2usinθg)cap R equals open paren u cosine theta close paren center dot cap T equals open paren u cosine theta close paren center dot open paren the fraction with numerator 2 u sine theta and denominator g end-fraction close paren Using the identity all important derivations of physics class 11 pdf download
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is the spring constant.The small amount of work done against this restoring force to extend the spring by
For a streaming, non-viscous, incompressible fluid, the total energy (pressure energy, potential energy, and kinetic energy) per unit volume remains constant along a streamline. Proving that work done equals the change in
For an incompressible, non-viscous fluid in streamline flow, the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit volume stays constant.
Proving that work done equals the change in kinetic energy ( Potential Energy of a Spring: Elastic Collisions: Finding the final velocities ( ) of two objects after a one-dimensional elastic collision. 4. Rotation and Gravity
ω2=gL⟹ω=gLspace omega squared equals the fraction with numerator g and denominator cap L end-fraction ⟹ omega equals the square root of the fraction with numerator g and denominator cap L end-fraction end-root Since time period 25 Most Important Derivations – Covers vectors, banking
y=usinθ(xucosθ)−12g(xucosθ)2space y equals u sine theta open paren the fraction with numerator x and denominator u cosine theta end-fraction close paren minus one-half g of open paren the fraction with numerator x and denominator u cosine theta end-fraction close paren squared
You can access these specific collections of derivations through the following links: – Detailed equations of motion and projectiles. 25 Most Important Derivations – Covers vectors, banking of roads, and collisions. EduRev Derivation Guides – Chapter-wise PDF downloads for motion and other topics. Comprehensive NCERT Derivation List – A 40-item checklist of all exam-ready derivations.
12m1u12+12m2u22=12m1v12+12m2v22⟹m1(u12−v12)=m2(v22−u22)--- (Eq 2)one-half m sub 1 u sub 1 squared plus one-half m sub 2 u sub 2 squared equals one-half m sub 1 v sub 1 squared plus one-half m sub 2 v sub 2 squared ⟹ m sub 1 open paren u sub 1 squared minus v sub 1 squared close paren equals m sub 2 open paren v sub 2 squared minus u sub 2 squared close paren space --- (Eq 2) Dividing Eq 2 by Eq 1 (
): Acceleration is defined as the rate of change of velocity:
of vector addition to find resultant magnitude and direction. Circular Motion: Centripetal Acceleration 2. The Rules of Engagement: Laws of Motion