Show that the kinetic energy of an object rotating about a fixed axis with angular momentum L = Iω can be written as K = L2/2I
Q: A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 s^ (-1) . The radius of…
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Q: Determine the magnitude of the angular momentum of a 100-kg particle when the position vector r =…
A: mass of particle = 100 kg position vector = 4i^ - 6j^ mvelocity = 3i^ - 8k^ m/s
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 solid sphere with radius 2.4m and mass of 77 kg has a moment of inertia given by2/5mr^2. It is…
A: 12Iω2=mg∆h1225mr2ω2=mg∆h ∆h=r2ω25g
Q: Problem ,. The figure below shows a two-dimensional body connected to the ground by two links AB and…
A: First locate the basic instantaneous centers by observation as shown in the figure.(if two links are…
Q: A uniform circular disc of mass m and radius R is rotating with angular speed w about an axis…
A: Given, θ=30° Kinetic energy, K=αmω2R2 I1=Izzcos30°I2=Ixxcos60°I1=Iyycos90°…
Q: Three identical point masses of m =0.1 (kg) are moving at a constant velocity v =10 (m/s)…
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Q: For the purposes of this problem, treat the Earth as a solid, uniform sphere with mass 5.97x1024 kg…
A: It is given that, M=5.97×1024 kgRe=6.37×106 mRo=1.5×1011 m
Q: The figure shows a device that can be used to measure the speed of a bullet. The device consists of…
A: Given that: angular displacement is θ=0.267 rad angular speed is ω=103 rad/s separation distance is…
Q: A light rod of length { = 1.00 m rotates about an axis perpendicular to its length and passing…
A: Given quantities: Length of the rod (L) = 1.00 m mass of particle 1 (m1) = 4.60 kg mass of particle…
Q: When the Sun runs out of nuclear fuel it will collapse into a white dwarf. The present radius of the…
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Q: 4.5 cm diameter uniform solid sphere has mass 110 g and is spinning at 1000 rpm. What’s its angular…
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Q: In the figure, two particles, each with mass m = 0.77 kg, are fastened to each other, and to a…
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Q: Consider a basketball player spinning a ball on the tip of a finger. If such a player performs 1.93…
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Q: Some European trucks run on energy stored in a rotating flywheel, with an electric motor getting the…
A: The kinetic energy of a rotating object is given by the equation K=12Iω2I is the moment of inertia…
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: In the figure, two particles, each with mass m = 0.82 kg, are fastened to each other, and to a…
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Q: A large door is a uniform rectangle, with height h and width w and mass m, which is free to rotate…
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Q: The disk with mass m = 2.5 kg and radius r= 20 cm rotates like a merry-go-round under the torque…
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Q: 2. A Lazy Susan (M=0.5 kg) in the shape of a disk is free to rotate about its center without…
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Q: Consider a particle A of mass ma = 9 kg moving at a velocity JA = 3 i + 3 j m/s and a particle B of…
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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: d from the eq
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Q: In the figure, two particles, each with mass m = 0.84 kg, are fastened to each other, and to a…
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Q: circular disc of mass M and radius R is rotating about its axis with angular speed ω1 . If another…
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Show that the kinetic energy of an object rotating about a fixed axis with
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- A hollow sphere (I=\frac{2}{3}mr^2I=32mr2) of radius R rotates about a diameter with an angular speed \omegaω. The sphere then collapses (magically) under the action of internal forces to a final radius of R/2 with no change in its mass. What is the final angular speed of the sphere?Assume mars is a uniform solid sphere of mass 6.42x10^23 kg and a radius 3390 km.The length of a day on mars is 24 hours and 37 min. What is the rotational kinetic energy of the planet about its axis.The figure shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance of d = 0.872 m, and rotating with an angular speed of 101 rad/s. The bullet first passes through the left disk and then through the right disk. It is found that the angular displacement between the two bullet holes is = 0.268 rad. From these data, determine the speed of the bullet. Number IN Bullet Units Motor
- A 26 g block sits at the center of a turntable that rotates at 50 rpm. A compressed spring shoots the block radially outward from the center along a frictionless groove in the surface of the turntable. Calculate the turntable's angular speed when the block reaches the outer edge. Treat the turntable as a solid disk with mass with mass 200 g and diameter 30.0 cm. Express your answer in revolutions per minute.A playground merry-go-round rotates like a large solid turntable about a fixed vertical axis, rotating at a rate of 0.65 rad/s. The moment of inertia of the turntable about this axis is 850 . A child of mass 40.0 k, initially standing at the center of the turntable, moves outward to a position 1.2 meters from the axis of rotation. Modeling the child as a particle, what is the new rotation rate of the merry-go-round?