Show that: If a particle is subject to a central force only, then its angular momentum is conserved i.e. If V(r) = V(r), then dL/dt = 0.

Q: If the length of the rod AB is 15 inches, and that a=25degrees, calculate the moment (Ib-in) about…

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Q: Set up an iterated integral moment of inertia about the y-axis of a triangular plate with vertices…

A: Given: The values are shown below:

Q: Determine by direct integration the mass moment of inertia and the radius of gyration with respect…

A: The equation of the curve is The radius of the elemental disc is given by Therefore,…

Q: Derive the relation for torque acting on system of particles from angular momentum 'L'?

A: we know that,

Q: Determine the minimum value of 0 for which the smooth cylinder shown remains in equilibrium.

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Q: Two particles, each of mass m and speed v, travel in opposite directions along parallel lines…

A: Solution:

Q: Priya is sitting on the edge of a horizontal circular plateform of radius 6m rotating with constant…

A: Velocity of Priya with respect to Rahul =  1 m/s

Q: A homogeneous steel wheel of radius R and mass M rolls without slipping on a horizontal rail, as…

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Q: Show that if a slab is rotating about a fixed axis perpendicular to the slab and passing through its…

A: Given  Angular speed of slab = ω Since , Linear momentum of slab about axis is zero. PG = mVG…

Q: (b) Calculate the angular momentum of Earth that arises from its orbital motion about the Sun,…

A: The moment of inertia I of a point particle is given by, I = mr2 where, m is the mass of the…

Q: The merry-go-round rotates at a constant angular velocity of w = 3,1 rad/s. Assume that an observer…

A: Constant Angular velocity (w) = 3.1 rad/s Radius (r) = 3.6 m

Q: A thin spherical shell of mass m and radius R rolls down a parabolic path PQR from a height H…

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Q: particle P of mass 2m can slide along a smooth rigid straight wire. The wire has one of its points…

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Q: Given, Tr = Tlr = Tlsin(0), at what angle 0 will torque be maximized?

A: As we know..  torque = r×F torque = rFSin(theta) ;

Q: Calculate the moment of interim Ip of the disk( without the point mass) with respect to point P, in…

A: Given that              The mass of the disk is = 2M so the moment of inertia due to the disk an…

Q: Determine the moments of the 3.4-kN force about point O and about point B.

A: Introduction: As the effect of force is to move body in translation as well as rotational motion.…

Q: Find the moment (Nm) caused by the force F = 803 N about point A if a = 27 mm and b = 31 mm.

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Q: A space of mass 120 kg is going to use a planet for a gravitational assist- that is, use the…

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Q: If you know the velocity of a particle, can you say anything about the particle’s angular momentum?

A: The angular momentum of a particle is dependent on the position vector (r) and the velocity(v) of…

Q: A thin spherical shell of mass m and radius R rolls down a parabolic path PQR from a height H…

A: Given that, the parabolic path PQR, where PQ is rough and QR is a smooth path. In rough path the…

Q: The velocity of the slider block C is 4 ft/s up the included groove. Determine the angular velocity…

A: For link BC, vc=(-4cos45oi^+4sin45oj^) ft/svB=-vBi^ω=ωBCk^rA/B=1i^ ft

Q: Calculate the magnitude of the angular momentum vector Of the moti on given by it's position P=…

A: SOlution: Given that r = 2i-3j m v = 4i m/s m = 1.5 kg

Q: Find the moment (Nm) caused by the force F = 618 N about point O if a = 26 mm and b = 38 mm.

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Q: Consider a solid sphere with mass m which starts from rest at the top of a frictionless fixed…

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Q: .* A rod of mass 5 kg and length 0.4 meters is held perfectly horizontal, but can rotate about a…

A: Write down the given values using suitable variables. Here m signifies rod mass, and L signifies…

Q: Find the Moment of in ertia of a regu lar solid circular cone of height (b)

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Q: Show directly that the time rate of change of the angular momentum about the origin for a projectile…

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Q: Does a ruler balance exactly at its midpoint? What does this imply about the mass distribution of…

A: Answer :-  Yes , ruler balance exactly at its midpoint

Q: What is the magnitude of angular momentum of JUST the partical circled to the system's mass center?

A: Mass of each particle (m)=0.5 kg Angular velocity of the body (ω)=2 rad/s Distance of the circled…

Q: Pa-QLs ka lang. Three identical point masses are ar- ranged to an equilateral triangle as shown. Let…

A: Given: Three identical masses are at the vertices of an equilateral triangle.

Q: d from the eq

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Q: Starting from rest at the top, a small sphere rolls without slipping off a large fixed sphere. At…

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Q: Match the conserved quantity with the symmetry of nature that is responsible.          -…

A: for every conservation law ,there is a symmetry.for every symmetry,there is a force field ,for every…

Q: Get the expression for the rotational of a vector field in spherical coordinates.

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Q: Write the equation for the conservation of angular momentum to the two bodies.

A: Introduction: The measure of the momentum in angular motion or the momentum of a body undergoing…

Q: Calculate the magnitude of the moment about the base point O of force F. *

A: Given data- Force F=800 lb           1lb=4.4452 newton so force F=(800)(4.4452 N) =3556.16 N

Q: Prove that the time rate of change of angular momentum is equal to the torque acting on the system…

A: Consider the moment of inertia of the system is I and the angular speed is ω. Write the equation for…

Q: Considering the disk with radius of r, constant rotational velocity of w, calculate the ratio…

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Q: If small particle 'm' is placed a distance 'x' from the central axis of a solid disk of total mass M…

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Q: Figure below shows a ring of mass m and radius r= 2.1 m rotating with an initial angular speed w,…

A: Solution: Given that mass =m radius = R=2.1 m point mass each m/8 the angular speed of the system =…

Q: A force P intersects the X axis at 4 ft to the right of O. If its moment about A is 170 ft-lb…

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Q: For a particle moving under a force field, a): Is the torque about the force zero? b): Is the…

A: Part a  For particle moving under a force field  Is the torque about the force zero false…

Q: A neutron star is a compact star that forms from the gravitational collapse of a very massive star.…

A: A neutron star is a star which has a collapsed core and the total mass lie with in a smaller radius…

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).