A rigid body of arbitrary shape rotates freely under zero torque. By means of Euler's equations show that both the rotational kinetic energy and the magnitude of the angular momentum are constant.

Q: A 2.5 kg particle located at (4, -2, -3)m moving in the negative y direction with a 4.2 m/s speed.…

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Q: A man of mass m=77kg runs at speed u= 5.0m/s along the tangent to a disk-shaped platform of mass…

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Q: A uniform rod of length L and mass M is free to rotate on a frictionless pin passing through one end…

A: As the conservation forces do work on the long rod, we use conservation of energy for this pure…

Q: A particle of mass m is under the central force created by the potential energy U(r)=A*r (A>0). The…

A: The effective potential as given in the question is  Ueff=L22mr2+Ar∂Ueff∂r=-2L22mr3+AAt minimum…

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

A: Solution:

Q: An airplane of mass 4.0 × 104 kg flies horizontally at an altitude of 10 km with a constant speed of…

A: a. consider that

Q: For a particle traveling in a straight line, are there any points about which the angular momentum…

A: The angular momentum can be expressed as

Q: Observe the relationship between torque and angular momentum.

A: Torque on a body τ ( in Nm)  ,about point O, given as…

Q: A particle moving in the x-y plane is subject to a central force F = f(r)Ã, where r = √x² + y² and F…

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Q: Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions.…

A: Given values -  Mass of Sun=Ms =1.99×1030 kgMass of Neutron=MN =2×MsMass of Neutron=MN =3.98×1030…

Q: A rigid body with one point fixed rotates with angular velocity omega and has angular momentum L.…

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Q: The four particles in Figure below are connected by rigid rods of negligible mass. The origin is at…

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Q: If a particle is moving with respect to a chosen origin it has linear momentum. What conditions must…

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Q: what that torque (r X F) should do to the direction of the angular momentum vector.

A: When a motorcycle is bending, it is ought to move on a circular path. So, there will be a…

Q: The figure shows three 0.01 kg particles that have been glued to a rod of length L=6 cm and…

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Q: In a double-star system, two stars of mass 4.9 x 1030 kg each rotate about the system's center of…

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Q: A particle undergoes uniform circular motion. About which point on the plane of the circle, will the…

A: A particle moves uniformly in a circle, as we know.We need to determine where on the circle's axis…

Q: The Earth’s mass is approximately 5.98 × 1024 kg, and it orbits the Sun at a distance of 1.50 × 1011…

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Q: A digital audio compact disc carries data along a continuous spiral track from the inner…

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Q: A large stone disk is viewed from above and is initially at rest as seen in the figure below. The…

A: mass (m) = 145 kg radius (r) = 2.2m F = 40 N t = 59 s

Q: Force F= (-7.5 N )i + (4.8 N) acts on a particle with position vector = (2.1 m )i + (3.3 m ) 7. What…

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Q: A 40-kg spool has a radius of gyration KG = 0.2 m. It rests on an inclined plane and a stopper A…

A: Given that: the mass of the spool is m=40 kg radius of gyration is kG=0.2 m the force is F=212.3 N…

Q: (a) Consider a person standing on a freely rotatable disk. He stretches his hands in horizontal…

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Q: Consider two blocks glued to the top of a disk that is turning at a non-zero angular speed, one…

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Q: A person who walks through the revolving door exerts a horizontal force of magnitude F-62 N on one…

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Q: A space station is to be constructed in the shape of a uniform hollow ring of mass M = 4,750 kg and…

A: Using conservative of angular momentum we can solve this

Q: A particle of mass m is under the central force created by the potential energy U(r)=A*r (A>0). The…

A: Solution: The effective potential energy of the central force motion is given by,  Ueff=L22mr2+Ur…

Q: In a double-star system, two stars of mass 2.7 x 1030 kg each rotate about the system's center of…

A: mass of each star (m) = 2.7×1030 kg radius (r) = 1.1×1011 m

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: (a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun.…

A: Given data M=5.97×1024 kgR=6.38×106 mr=1.5×1011 mT=365 days

Q: Vectors are an important part of the language of science, mathematics, and engineering. They are…

A: The conditions provided are:A. x>0,y>0, B. x>0,y<0C. x<0,y>0D. x<0,y<0These…

Q: Two astronauts, each having a mass M, are connected by a rope of length d having negligible mass.…

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Q: The figure shows three 0.0147 kg particles that have been glued to a rod of length L=6.01 cm and…

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Q: In the figure, a 0.400 kg ball is shot directly upward at initial speed 50.0 m/s. What is its…

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Q: A point particle travels in a straight line at constant speed, and the closest distance it comes to…

A: A point particle travels in a straight line at constant speed, and the closest distance it comes to…

Q: A force vector (2, -1, 4)N acts on a particle at the position (1, -3, 0)m. What is the torque due to…

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Q: A particle of mass m is dropped from rest at t = 0 at the point (−d, 0, 0) and falls vertically in…

A: given  free falling particle under earth’s gravitational field  required:) (1) expression for…

Q: The end state of our Sun will most likely be a white dwarf star. It would have about one fourth of…

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Q: The figure shows three 0.0186 kg particles that have been glued to a rod of length L=5.67 cm and…

A: Given: Mass of the three particles, M = 0.0186 kg Length of the rod, L = 5.67cm = 0.0567 m Distance…