A spinning figure skater who brings their arms close in to their body will then spin faster. The stick person figure skater we're looking at has a mass of M - 50 kg and arms of length Ri 0.8 m. The skater originally spins with angular speed w; = 2 radians/second, and has their arms fully extended. At this initial state, the figure skater can be modeled as a hollow cylinder with moment of inertia I = MR²\ = When the skater brings their arms in towards their body, they can be modeled as a solid cylinder with radius Rf = 0.2 m. ਲੋਕ ਗੀਤ wf Uj Determine the final angular speed wf of the skater when their arms are tucked in.

Everyone's favorite flying sport disk can be approximated as the combination of a thin outer hoop and a uniform disk, both of diameter Da = 0.273 m. The mass of the hoop part is mh = : 0.120 kg and the mass of the disk part is md = 0.050 kg. Imagine making a boomerang that has the same total moment of inertia around its center as the sport disk. The boomerang is to be constructed in the shape of an "X," which can be approximated as two thin, uniform rods joined at their midpoints. If the total mass of the boomerang is to be m₁ = 0.235 kg, what must be the length Lы of the boomerang? | I Lb = = Cross-sectional view m

Three small objects are located in the x-y plane as shown in the figure. The objects have the following masses: MÃ 1.45 kg, mB = 2.99 kg, mc = 3.07 kg. = y (m) 9 8 7 6 4 3 2 1 0 H 01 2 3 5 6 7 8 9 4 x (m) What is the moment of inertia of this set of objects with respect to the axis perpendicular to the the x-y plane passing through location x = 5.00 m and y 4.00 m? The objects are small in size, their moments of inertia about their own centers of mass are negligibly small.

A ball (in the form of a spherical shell which has a moment of inertia of 2/3 M R^2) rolls down a roof, then falls to the ground. The ball has a mass of 1.65 g and a radius of 15.0 cm. The roof is inclined at 20.0 degrees and the ball rolls a distance of 3 meters along the roof before falling off. a)  What is the angular speed of the ball at the moment it leaves the roof? b)  If the distance from the end of the roof to the ground is 2.50 m, how many revolutions does the ball make before it hits the ground?

Consider a person who is sitting on a frictionless rotating stool. The person initially has his arms outstretched and is rotating with an angular speed of 5.0 rad/s. He then pulls his arms close to his body, thus reducing his moment of inertia to 80% of the initial one. What is his final angular speed?

A horizontal vinyl record of mass 0.0855 kg and radius 0.101 m rotates freely about a vertical axis through its center with an angular speed of 4.18 rad/s and a rotational inertia of 2.64 x 10-4 kg·m2. Putty of mass 0.0253 kg drops vertically onto the record from above and sticks to the edge of the record.What is the angular speed of the record immediately afterwards?

The figure above shows two barbells, which can be modeled as two point masses connected by a massless rod. In the figure, L = 0.77 m and m = 20.1 kg. The barbells can rotate about an axis that is perpendicular to the rod and passes through the midpoint of each rod. For the barbell with the larger moment of inertia, give the moment of inertia (in units of kg m2).

The object shown below is centered on the origin, and has a width of 20 cm in the x direction, 3 cm in the y direction, and 5 cm in the z direction. Around which axis does it have the lowest moment of inertia l?

Modern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a great amount of angular momentum when rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 15 rpm. Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.

There is a circular disk of radius 0.5 m and mass 2 kg. A child throws down a rock, hitting the edge of the disk perpendicularly with a force of 50 N. Thedisk doesn't break, but starts to spin. If the moment of inertia for the circular disk rotating about the center is 1/2M(r^2), What is the tangential acceleration of a point on the disk 0.05 m from the point of impact?