A uniform rod of mass 2.00 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m, = 5.40 kg is attached to one end and a second mass m, = 2.20 kg is attached to the other end of the rod. Treat the two masses as point particles. (a) What is the moment of inertia of the system? kg - m2 (b) If the rod rotates with an angular speed of 2.60 rad/s, how much kinetic energy does the system have? (c) Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined? | kg - m² (d) If the rod is of negligible mass, what is the kinetic energy when the angular speed is 2.60 rad/s?

On average, both arms and hands together account for 13% of a person's mass, while the head is 7.0% and the trunk and legs account for 80%. We can model a spinning skater with her arms outstretched as a vertical cylinder (head, trunk, and legs) with two solid uniform rods (arms and hands) extended horizontally. Suppose a 75.0 kg skater is 1.80 m tall, has arms that are each 66.0 cm long (including the hands), and a trunk that can be modeled as being 33.0 cm in diameter. If the skater is initially spinning at 82.0 rpm with her arms outstretched, what will her angular velocity ?2 be (in rpm) after she pulls in her arms and they are at her sides parallel to her trunk? Assume that friction between the skater and the ice is negligble.

A woman with mass 50 kg is standing on the rim of a large disk that is rotating at 0.50 rev/s about an axis through its center. The disk has mass 110 kg and radius 4.0 m. Calculate the magnitude of the total angular momentum of the woman-disk system. (Assume that you can treat the woman as a point.)

A uniform thin rod of mass ?=3.47 kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass ?=0.277 kg, are attached to the ends of the rod. What must the length ? of the rod be so that the moment of inertia of the three-body system with respect to the described axis is ?=0.987 kg·m2 ?

A person having a mass of 75 kgkg sits on the edge of a horizontal rotating platform, 2.1 mm from the center of the platform, and has a tangential speed of 2.6 m/sm/s. Calculate the angular momentum of the person. Express your answer to two significant figures and include the appropriate units.

Two children  (m = 29.0 kg  each) stand opposite each other on the edge of a merry-go-round. The merry-go-round, which has a mass of 1.70 ✕ 102 kg and a radius of 1.6 m, is spinning at a constant rate of 0.48 rev/s. Treat the two children and the merry-go-round as a system. (a) Calculate the angular momentum of the system, treating each child as a particle. (Give the magnitude.) kg · m2/s(b) Calculate the total kinetic energy of the system. J(c) Both children walk half the distance toward the center of the merry-go-round. Calculate the final angular speed of the system. rad/s

Each of the following objects has a radius of 0.181 m and a mass of 2.31 kg, and each rotates about an axis through its center (as in this table) with an angular speed of 38.3 rad/s. Find the magnitude of the angular momentum of each object. (a) a hoop kg - m²/s (b) a solid cylinder kg. m²/s (c) a solid sphere kg - m²/s (d) a hollow spherical shell kg - m²/s

A massless string is wrapped around a solid 7.6-kg cylinder of diameter 24 cm that can rotate freely withoutfriction about an axis through its center. A stone is tied to the loose end of the string. When the stone isreleased from rest, the cylinder turns without the string slipping. If the cylinder has an angular velocity of26 rad/s after 1.4 s, what is the mass of the stone? Through how many revolutions does the cylinder turn inthis time?

A cord is wrapped around the rim of a wheel 0.225 m in radius, and a steady pull of 41.5 N is exerted on the cord. The wheel is mounted on frictionless bearings on a horizontal shaft through its center. The moment of inertia of the wheel about this shaft is 5.50 kg m² 世 Prov

A space probe in outer space has a gyroscope within it used for rotation and stabilization. The moment of inertia of the gyroscope is I, = 24.5 kg • m about the axis of the gyroscope, and the moment of inertia of the rest of the space probe is I, = 5.00 x 105 kg · m2 about the same axis. Initially both the space probe and gyroscope are not rotating. The gyroscope is then switched on and it nearly instantly starts rotating at an angular speed of 150 rad/s. How long (in s) should the gyroscope operate at this speed in order to change the space probe's orientation by 26.0°?