A) Show that K.E can be expressed can be expressed a sum of K.E of motion of center of mass and K.E of motion about center of mass.?

Q: shown below, a bullet of mass m and speed v is fired at an initially stationary sphere. The bullet…

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Q: What is the magnitude of the angular momentum relative to the origin of the 200 g particle in the…

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Q: Suppose a piece of dust finds itself on a CD. If the spin rate of the CD is 360 rpm, and the piece…

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Q: A satellite describes an elliptic orbit about a planet of mass m . Denoting by r0 and r1 ,…

A: M = mass of the planet m = mass of the satellite r0 = minimum distance of the satellite from the…

Q: Mars has a mass 0.642 x 1024 kg and a radius of 1700. kg. On average, it is 228 x 106 km from the…

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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: onsider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its…

A: as per rule solve 3 parts

Q: Three identical particles of mass m are making a common uniform circular motion with the period T…

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Q: A space station consists of a large, lightweight ring of radius R = 60 m and two small heavy control…

A: R = 60 m M= 50000 kg a) Moment of inertia of space station = 2 M R 2  = 2 * 50000 * (60)2  = 3.6 *…

Q: Gravitational Slingshot

A: Given,

Q: The 100 kg sphere A is released from rest at an angle of α from the vertical, and hits the 10 kg…

A: Given data: The mass of sphere m=100 kg. The mass of the block is M=10 kg. The initial velocity of…

Q: A particle of mass m is dropped at the point (−d, 0) and falls vertically in Earth’s gravitational…

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Q: 9. Assuming that the gravitational acceleration inside a homogeneous spherical shell is zero, show…

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Q: two rockets of masses m1 = 100000kg and m2 = 200000kg are in empty spacde and are connected by a…

A: In this question we are given that two rockets of masses m1 = 100000kg and m2 = 200000kg are in…

Q: find the mass of Planet X.   b) Suppose that at the moment the spacecraft reaches its maximum…

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Q: speed at perigee

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Q: The 100 kg sphere A is released from rest at an angle of α from the vertical, and hits the 10 kg…

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Q: (a) Find the radius of the circular orbit of a satellite moving with an angular speed equal to the…

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Q: 2) The mass of a rocket is m, and its radius of gyration about the mass center C is kc. Determine…

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Q: A projectile of mass m is launched with an initial velocity v, making an angle 0 with the horizontal…

A: The angular momentum of a projectile varies with time as L = (1/2) x m x vi x g x cos(θ) x t2

Q: Concerning the life of an individual comet, say, from the Kuiper Belt or Oort Cloud.  These objects…

A: We know that the angular momentum must remain conserved. Here lets say that  m = mass of the comet v…

Q: When kicking a football, the kicker rotates his leg about the hip joint. (a) If the velocity of the…

A: a) Angular velocity is given as,

Q: The centrifuge at NASA Ames Research Center has a radius of 8.8 m and can produce forces on its…

A: Given Radius of the arm R = 8.8 m Initial ass of the payload M = 20 kg Initial acceleration a = 10g…

Q: A person of mass M stands on a bathroom scale inside a Ferris wheel compartment. The Ferris wheel…

A: Given A person of mass M stands on a bathroom scale inside a Ferris wheel compartment. The Ferris…

Q: As shown below, a bullet of mass m and speed v is fired at an initially stationary sphere. The…

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Q: A jet flies straight at a speed of 80 m / s at an altitude of 1300 m above the z surface. The mass…

A: Given, m=1200kg v=80m/s r=1300m   Angular Momentum = mvr

Q: You may want to review (Pages 321 - 323) Part A What is the magnitude of the angular momentum of the…

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Q: A satellite is to be completely despin using a two mass's Yo-Yo device with tangential release.…

A: The radius of the spacecraft is, r=d2=240 cm2=120 cm0.01 m1 cm=1.2 m The velocity of the Yo Yo…

Q: Suppose that an asteroid traveling straight toward the center of the earth were to collide with our…

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Q: The 2.0 kg, uniform, horizontal rod shown is seen from the side. What is the gravitational torque…

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Q: Comet Hale-Bopp has an orbit about the Sun with eccentricity e=0.9951 and semimajor axis a=186.5 AU.…

A: The orbit has eccentricity e=0.9951 - Elliptical orbit with semimajor axis a=186.5 au=2.79*1013 m.…

Q: Find the center of gravity for the distribution of masses (red circle) given as in the figure? Where…

A: The value of the acceleration due to gravity is the same for all the masses.

Q: As shown below, a bullet of mass m and speed v is fired at an initially stationary sphere. The…

A: (given) m is the mass of the bullet, v is the speed of bullet, M is the mass of sphere. Conservation…

Q: Two solid spheres of radius R and mass m are initially separated by a distance d such that the two…

A: Gg

Q: A satellite in a geosynchronous circular orbit is 42,164.0 km from the center of Earth. A small…

A: According to conservation of angular momentum is, the initial angular momentum is equal to the final…

Q: particle of mass m is dropped from a height h, located at latitude λ (north), find an expression for…

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Q: Calculate the angular momentum (in kg · m2/s) of Mercury in its orbit around the Sun. (The mass of…

A: Data Given ,  The mass of the mercury ( m ) = 3.3 × 1023 kg Orbital radius ( r ) = 5.790 × 107 km =…

Q: Suppose a piece of dust finds itself on a CD. If the spin rate of the CD is 380 rpm, and the piece…

A:

Q: .Determine the speed of the satellite in terms of G, h, RE (the radius of the Earth), and ME (the…

A: SOlution: Given that To Determine the speed of the satellite in terms of G, h, RE (the radius of the…

Q: A space station out beyond the solar system is rotating with constant angular velocity. A spaceship…

A: As the ship come along the diameter of the space station. So it do not apply any torque to the space…

Q: A system consists of two objects of mass 2m and m, connected by a rod of negligible mass as shown.…

A: The rod connecting the two objects is massless. The gravitational force between 2 masses can be…

Q: A race car starts from rest in the pit area and accelerates at a uniform rate to a speed of 37 m/s…

A: Write the given values with suitable variables. v=37 m/st=15 sr=500 mm=950 kg Here, v denotes the…

Q: sphere of radius R and mass M is spinning about its center with an initial angular velocity ωi. The…

A: Sphere of radius R and mass M is spinning about its center with an initial angular velocity ωi. The…

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.