A 3.00 kg solid sphere with a radius of 15 cm is rolling without slipping along a horizontal floor. The magnitude of the velocity of the center of mass is 3.00 m/s. What 2. is the ratio of the sphere's rotational kinetic energy to its translational kinetic energy, KErot / KEtrans?
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- A figure skater rotating at 50.00 rad/s with arms extended has a moment of inertia of 4.5 kg. m^2. If the arms are pulled in so the moment of inertia decreases to 1.80 kg. m^2, what is the final angular speed? O 17.6 rad/s 12.25 rad/s 0.125 rad/ s 0.81 rad/s 125 rad /sIn orbit mechanics, the angular momentum is also an important quantity governing the satellite's motion. Assume planar motion, a satellite is orbiting around Earth center within a fixed plane. Thus it's motion is completely described by the distance r and the angle (relative to some reference direction). êo 0 (center of Earth) êr PO.. P (satellite) satellite's trajectory Obtain the satellite's angular momentum with respect to Earth center. For spacecrafts, the angular momentum (h) is h = Fx, it is independent of mass. What is the magnitude of h?T m A 25.0 kg mass is hung from a rope that is passed over a pulley and held by a man standing on a ramp. The pulley can be treated as a solid disk with a mass of 10.0 kg that has a radius of 0.400 m. The man pulls the rope so that the pulley rotates from rest through an angular displacement of 15.0 rad in 2.00s. A. What is the angular acceleration of the disk? B. What is the tension of the rope as it pulls up on the box? C. What is the force applied by the man on the rope as he pulls the box upward?
- 3 1. A uniform solid sphere rolls without slipping down a 28° inclined plane. What is the acceleration of the sphere's center of mass? The moment of inertia of a uniform solid sphere about an axis that passes through its center = mr². The moment of inertia of a uniform solid sphere about an axis that is tangent to its surface = 7/5mr². m/s² E D C 4 22 R F % 5 V T G tv B MacBook Air 22 Y H 7 5 N 00 8 ZA 3 ( 9 K MOSISO O O V P command DUI 04 M optionA spherical shell with a mass of 1.43 kg and a radius of 0.39 m is rolling across the level ground with an initial angular velocity of 35.9 rad/s. It is slowing at an angular rate of 2.6 rad/s². What is its rotational kinetic energy after 4.7 s? The moment of inertia of a spherical shell is I = 글MR2A disk of radius 0.5 m is rotating with constant angular acceleration around an axis passing through its center as shown in the figure. It starts rotation at r = 0 with an angular velocity of 10 rad/s/ After making 30 revolutions, its angular velocity becomes 100 rad/s. Find the tangential acceleration (in m/s) of a point P on the rim of the disk P R
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