A uniform rectangular block has mass M and sides 2a, 2b and 2c. Find the principal moments of inertia of the block (i) at its centre of mass, (ii) at the centre of a face of area 4ab. Find the moment of inertia of the block (i) about a space diagonal, (ii) about a diagonal of a face of area 4ab.

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A: Introduction: Given data: Length of the rod is, L=0.6 m Mass of the rod is, M= 1.6 kg The point mass…

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A: Given:mass of the disk, m = 133 kgradius of the disk, r = 1.79 mmass of the person, mp = 61.7…

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Q: he x, y, and z axes, with one end of each at the origin. Given I = 1/12 ML2 for a rod pivoted about…

A: Given: I=112ML2

Q: A 103 kg horizontal platform is a uniform disk of radius 1.71 m and can rotate about the vertical…

A: mass of the uniform disc=103Kg Radius of the disc=1.71 m Moment of inertia of the disc,I=12MR2   (…

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Q: 129-kg horizontal platform is a uniform disk of radius 1.61 m and can rotate about the vertical axis…

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Q: our objects are held in position at the corners of a rectangle by light rods. m1 (kg) m2 (kg) m3…

A: Given:- Four objects are held in position at the corners of a rectangle by light rods. m1 (kg) m2…

Q: Four identical spheres of masses 2.0 kg each and radius 0.25 m are situated at the four corners of a…

A: Given:         m=2.0kgradius,r=0.25m To find: Moment of inertiaa)passing through centre of the…

Q: Suppose we want to calculate the moment of inertia of a 56.5 kg skater, relative to a vertical axis…

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Q: 4. Four point masses, m1 1 kg, m2 = 2 kg, m3 = 3 kg and m4 = 4 kg are on the x axis as shown in the…

A: Moment of inertia of the system is equal to the sum of individual moment of inertia of the masses. #…

Q: A particle is acted on by two torques about the origin: t1 has magnitude of 2.0 Nm and is directed…

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Q: The position vector of a 2.5 kg particle is given by r=4.0 i +3.0 fĵ, where r is in meters and t is…

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Q: A box and a solid cylinder of equal mass M are moving across horizontal surfaces which are joined to…

A: Answer: This problem is based on the energy conservation. When the objects move on the horizontal…

Q: uniform rod of mass 3.4 kg is 4 m long. The rod is pivoted about a horizontal, frictionless pin at…

A: Given,Mass of the rod, m = 3.4 kglength  of the rod, l = 4 mθ = 70°acceleration due to gravity, g =…

Q: A 101 kg horizontal platform is a uniform disk of radius 1.61 m and can rotate about the vertical…

A: Given Mass of horizontal platform = 101 kg (uniform disk ) Radius of platform = 1.61 m Mass of a…

Q: 119 kg horizontal platform is a uniform disk of a radius of 1.97 m and can rotate about the vertical…

A: Moment of inertia of this system is given as I=Idisk +Idog+Iperson We know that Idisk=0.5M1R12…

Q: 20

A: Given:

Q: A particle of mass 4.0 kg has position vector of (4.0i+3.0j) at a particular instant of time when…

A: mass m= 4 kg x=4i+3j v=3i mv=12i

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Q: At one instant, force F 1.49ĵ N acts on a 0.982 kg object that has position vector 7 = (5.89î –…

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Q: A solid ball rolls up a ramp (inclined plane) of h=0.50 m high withou slipping. It has an initial…

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Q: A 103 kg horizontal platform is a uniform disk of radius 1.71 m and can rotate about the vertical…

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Q: Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius…

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Q: Assume that (1) F = 10i +60j - 20k, acting at a point (8, 6, 4), and (2) two end points of a line L…

A: Given data The vector equation of force 1 is F1 = 10i +60j - 20k acting at a point (8, 6, 4). The…

Q: (a) Calculate the angular momentum (in kg·m2/s) of an ice skater spinning at 6.00 rev/s given his…

A: a)Angular momentum = moment of inertia * angular speed  = 0.35 * (6 * 2π) = 13.2 kg m2 /sb)Using…

Q: A 7.62 kg particle with velocity = (9.74 m/s )î - (2.04 m/s ) Ĵ is at x = 3.16 m, y = 9.00 m. It is…

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Q: 4 V3ga(v²-1) - Umin 16 ga 3 (v2 -1) Vmin 8, V§ga(v2-1) - Umin 4 V7ga(v2-1) - Umin 3ga (v2– 1) (V2 –…

A: For this given problem, Concept used -  Conservation of angular momentum Conservation of energy

Q: The moment of inertia I of a cheap door of mass M= 4.00 kg (about an axis going through the hinges…

A: Given that:M=4.00 kgR=0.960 mI=13MR2m=0.300 kgvi=20.0 m/sIm=mR2

Q: Take an equilateral triangular sheet of side and remove the "middle" triangle (1/4 of the area).…

A: Here, the scaling arguments and parallel-axis theorem will be used to compute the moment of inertia.…

Q: A 117 kg horizontal platform is a uniform disk of radius 1.67 m and can rotate about the vertical…

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Q: Two kids, each with a mass of 25.0 kg, are standing at the edge of a merry-go-round. Treat both kids…

A: Given data The mass of the kid is: m= 25 kg The mass of the merry-go-round is M = 97.5 kg The disk's…

Q: A 12-lb force P is applied to the control rod AB as shown. Knowing that the length of the rod is 5…

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Q: Assume that the physical pendulum in a grandfather's clock is composed of a uniform rod (mass mrod =…

A: Given, mass of rod, mrod=5M length of the rod, Lrod=10R mass of disk, mdisk=M the radius of the…

Q: Assume that the physical pendulum in a grandfather's clock is composed of a uniform rod (mass mrod =…

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Q: John McClane, desperately trying to escape the bad guys in an upper floor of a skyscraper, grabs a…

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