Fdown=m⋅g=(Volume×Density)⋅g=(πr2hρ)⋅gspace cap F sub d o w n end-sub equals m center dot g equals open paren Volume cross Density close paren center dot g equals open paren pi r squared h rho close paren center dot g Equilibrating the upward and downward forces:
∫uvvdv=∫0sadsintegral from u to v of v space d v equals integral from 0 to s of a space d s :
: Derivation of the Magnitude and Direction of the Resultant vector using the Parallelogram Law and Triangle Law. Laws of Motion & Work-Energy Centripetal Acceleration : Derivation of for a body in uniform circular motion. Banking of Roads : Finding the maximum safe velocity for a vehicle on a banked road with friction. Work-Energy Theorem
This chapter introduces why things move. Focus on the core mechanics of force and friction: Newton’s Second Law:
didn't just show the math; it showed the geometry as a dance of vectors. The Banking of Roads all important derivations of physics class 11 pdf download
: Proving that work done is equal to the change in kinetic energy.
12gT2=(usinθ)Tspace one-half g cap T squared equals open paren u sine theta close paren cap T
0=(usinθ)2−2gHspace 0 equals open paren u sine theta close paren squared minus 2 g cap H
Fup=Tcosθ⋅(2πr)space cap F sub u p end-sub equals cap T cosine theta center dot open paren 2 pi r close paren 12gT2=(usinθ)Tspace one-half g cap T squared equals open
For a planar, two-dimensional object, the moment of inertia about an axis perpendicular to its plane ( Izcap I sub z
When an object is thrown obliquely near the Earth's surface, it moves along a curved path under constant gravity.
Applying the law of conservation of linear momentum. 4. Work, Energy, and Power
dL⃗dt=(v⃗×mv⃗)+r⃗×F⃗space the fraction with numerator d modified cap L with right arrow above and denominator d t end-fraction equals open paren modified v with right arrow above cross m modified v with right arrow above close paren plus modified r with right arrow above cross modified cap F with right arrow above Because the cross product of parallel vectors is zero ( Conservation of Linear Momentum
[v]uv=a[t]0tspace open bracket v close bracket sub u to the v-th power equals a open bracket t close bracket sub 0 to the t-th power v−u=atspace v minus u equals a t v=u+atspace v equals u plus a t 2. Second Equation of Motion: Velocity ( ) is the instantaneous rate of change of displacement ( v=dsdtspace v equals d s over d t end-fraction ds=v⋅dtspace d s equals v center dot d t Substitute
mole of an ideal gas be heated at constant volume. The heat supplied is .By the First Law of Thermodynamics:
Finding a comprehensive list of is often the turning point for Class 11 students. While the numericals get a lot of attention, the derivations are the "skeleton" of the subject—they show you exactly how we get from a basic concept to a final, usable formula.
∫uvdv=a∫0tdtintegral from u to v of d v equals a integral from 0 to t of d t
. After a perfectly elastic collision, their velocities become 1. Conservation of Linear Momentum