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A skater is spinning about a fixed symmetrical vertical axis. When she lifts her arms above her head, her moment of inertia about this axis of rotation drops from 12.0 kg m2 to 8.00 kg m2. What is the ratio of her final rotational energy and her initial rotational energy?

A person pushes on a lever 0.7 meters away from the axis of rotation with 100 N of force. The rotational inertia of the lever is 35 kg*m2. Calculate the angular acceleration of the lever.

A uniform rod is set up so that it can rotate about an axis at perpendicular to one of its ends. The length and mass of the rod are 0.893 m and 1.19 kg, respectively. A force of constant magnitude F acts on the rod at the end opposite the rotation axis. The direction of the force is perpendicular to both the rod's length and the rotation axis. Calculate the value of F that will accelerate the rod from rest to an angular speed of 6.31 rad/s in 8.87 s. F = N

One end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m, as shown in the figure below. When θ = 23.0°, the speed of the object is 5.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An arrow labeled vector v points in the direction of motion. (a) At this instant, find the magnitude of the tension in the string.Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N(b) At this instant, find the tangential and radial components of acceleration. at = Your response differs from the correct answer by more than 100%. m/s2 downward tangent to the circle ac = Your response differs from the correct answer by more…

Consider two boxes initially at rest as shown, each of mass 5.0 kg, that are connected by a massless string over a pulley of radius 5.0 cm and rotational inertia equal to 4.0 x 10-3 kg·m². The coefficient of kinetic friction between the inclined surface and the box is 0.15. Find the speed of the boxes just after they have moved 1.0 m. Justify approach taken as you begin your solution. 30° m m

A turntable (disk) of radius r = 27.0 cm and rotational inertia 0.440 kg · m2 rotates with an angular speed of 2.98 rad/s around a frictionless, vertical axle. A wad of clay of mass m = 0.242 kg drops onto and sticks to the edge of the turntable. What is the new angular speed of the turntable? (A) _______ rad/s

Two blocks are connected by massless string that is wrapped around a pulley. Block 1 has a mass m1=6.00 kg, block 2 has a mass m2=2.00 kg, while the pulley has a mass of 1.00 kg and a radius of 18.0 cm. When the pulley turns, there is friction in the axel that exerts a torque of magnitude 0.410 N m. If block 1 is released from rest at a height h=1.40 m, how long does it take to drop to the floor?

A tire is tied to a rope that is tied to the branch of a tree so that the tire swings in a circular trajectory of radius h1 = 15.31 m. A child takes the tire to the top of a platform that is a height h2 = 12.60 m above the ground, sits in the tire, and swings from rest from the platform. The combined mass of the tire and child is 36 kg. The rope is taut when the child leaves the platform and you may neglect the mass of the rope. At the bottom of the circular trajectory, the child and tire are a height h3 = 0.99 m above the ground. include a diagram showing the physical sites (a) Calculate the speed of the child/tire at the bottom of the circular trajectory.  m/s (b) Calculate the maximum tension in the rope as the child/tire swing back and forth.  N

A uniform rod is set up so that it can rotate about an axis at perpendicular to one of its ends. The length and mass of the rod are 0.765 m and 1.27 kg respectively. A force of constant magnitude ?F acts on the rod at the end opposite the rotation axis. The direction of the force is perpendicular to both the rod's length and the rotation axis. Calculate the value of ?F that will accelerate the rod from rest to an angular speed of 6.21 rad/s in 9.91 s