A cylinder of mass M, radius R, and moment of inertia I, rolls down the slope of angle alpha. Write down the lagrangian and solve it for the cylinders accel

Q: imperfectly rough fixed A homogeneous sphere rolls down an sphere, starting from rest at the highest…

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Q: Let S be a non-uniform scaling transformation and R be a rotation transformation. Consider the…

A: Scaling transformation.

Q: Use qualitative arguments (i.e., draw surfaces and/or loops on the plots and ascribe mcaning to the…

A: Loop drawn in the diagram shows that vector field has non zero divergence since net arrows are…

Q: 1 2 Vi-v/² = 1 + 1 m²c? 2,2

A: 11-v2/c22=1+P2m2 c2 where,  v-velocity, c-velocity of light, p-momentum, m-mass To prove this…

Q: In a clamped frictionless pipe elbow (radius R) glides a sphere (weight W = mg) with zero initial…

A: Using Newtons law, we get,

Q: A triangle in the xy plane is defined with = (0,0), (0, 2) and corners at (x,y) (4, 2). We want to…

A: The triangle has corners at (x,y)=(0,0), (0,2) and (4,2). We have a function f(x,y) which we need to…

Q: L,, Ly] = L,Ly – LyL = ihL, %3D %3D

A: We know, Lx^=y^pz^-z^py^Ly^=z^px^-x^pz^Lz^=x^py^-y^px^

Q: Calculate the commutators [^px, ^x2].

A: Calculate commutator of px with x^2

Q: A A T4!= "T7-"T7= "77

A: The angular momentum of x  and z component is defined as…

Q: Find the expressions for the car- tesian components and the angular momentum measure L = (Lx, Ly,…

A: Find the expressions for the cartesian components and the angular momentum measure L = (Lx, Ly, Lz)…

Q: Calculate the commutators [^px2, f(^x

A: Find commutator of px with x^2

Q: Find the answer for the given: Let L be the length. Let M be the mass. A rod that has L and M was…

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Q: Steiner’s theorem and gyration radius. A metal tank wheel in the shape of a disc of radius R is…

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Q: If Qj is the generalised force and ògj is the virtual displacement in the generalised coordinate gi,…

A: If Qj is the generalised force associated with the virtual displacement δqj associated with it then…

Q: Find the divergence of the position vector r. Also find V - for r + 0. Repeat both 3 tasks, but now…

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Q: An AC voltage of 12.0 V is applied to the primary of a transformer that has 3 times as many turns in…

A: The equation for a transformer is given by VPVS=NPNS  (1) Here, VP is the voltage in primary coil,…

Q: The spherical harmonics are the eigenfunctions of ?̂2 and ?̂ ? for the rigid rotor and thehydrogen…

A: The objective of this question is to determine the angles at which nodal surfaces will occur for the…

Q: For the inner product (|4) the left side o always be the conjugate value O True O False

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Q: The resultant of two vectors is 20 units long and makes angles of 20o and 50o with the two vectors,…

A: Given, Length of resultant,R=20 units Angle of resultant with vectors,θ1=20°,θ2=50°

Q: Q. Derive the relation betueen unit Vectors of Cylindrical and Cartesian Coordinates?

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Q: U sing the rules of B olo gnese algebra Demoreken's theorem, s implify the following Booleah ex…

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Q: B=re-²9, find curl(B) analytically. Compare the value of the divergence at points P1 = (x1, y1) =…

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Q: Using Lagrangian formalism, solve the following problem: A solid cylinder is released from rest to…

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Q: 1. Consider the van der Waals equation (1) а + v2) (Vm – b) – RT = 0 - V2 т where p, Vm, T, are,…

A: Given,Van der Waals equation,p+aVm2Vm-b-RT =0p is the pressureVm is the molar volumeT is the…

Q: Find the moments Mz, My and the mass m, of the triangular lamina defined by the vertices (0,0),…

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Q: Angular momentum plays a key role in dealing with central forces because it is constant over time.…

A: We have, L→=r→×p→ By the nature of cross product, the two properties that L→ has: L→ is a vector…