A student sits on a rotating stool holding two 3.3-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg · m2 and is assumed to be constant. The student then pulls in the objects horizontally to 0.43 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the student before and after the objects are pulled in

A girl of mass 20.3 kg stands on the rim of a frictionless merry-go-round of radius 1.29 m and rotational inertia 455 kg-m2 that is not moving. She throws a rock of mass 584 g horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground, is 5.22 m/s. Afterward, what are (a) the angular speed of the merry-go-round and (b) the linear speed of the girl? (a) Number i Units (b) Number i Units

A student sits on a rotating stool holding two 3.20-kg objects. When his arms are extended horizontally, the objects are 1.00 m from the axis of rotation and he rotates with an angular speed of 0.750 rad/s. The moment of inertia of the student plus stool is 3.00 kg • m and is assumed to be constant. The student then pulls in the objects horizontally to 0.490 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the system (student/stool/objects) before and after the objects are pulled in. before J after

A small 0.340-kg object moves on a frictionless horizontal table in a circular path of radius 1.10 m. The angular speed is 7.09 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 108 N, what is the radius of the smallest possible circle on which the object can move? Number Units

A space station shaped like a giant wheel has a radius 103 m and a moment of inertia of 4.97 x 108 kg-m². A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1 g. When 100 people move to the center of the station for a union meeting, the angular speed changes. What acceleration is experienced by the managers remaining at the rim? Assume that the average mass of each inhabitant is 65.0 kg. m/s²

A student sits on a rotating stool holding two 4.0 kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation, and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg-m? and is assumed to be constant. The student then pulls the objects horizontally to 0.20 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the student system before and after the objects are pulled in. before after

An old millstone, used for grinding grain in a gristmill, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 300 N applied to its edge causes the wheel to have an angular acceleration of 0.880 rad/s2. (a) What is the moment of inertia of the wheel (in kg · m2)? kg · m2   (b) What is the mass (in kg) of the wheel? kg   (c) The wheel starts from rest and the tangential force remains constant over a time period of 5.50 s. What is the angular speed (in rad/s) of the wheel at the end of this time period? rad/s

Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 125 kg-m². When one person is standing on the carousel at a distance of 1.50 m from the center, the carousel has an angular velocity of 0.600 rad/s. However, as this person moves inward to a point located 1.01 m from the center, the angular velocity increases to 0.800 rad/s. What is the person's mass? m = i

A student sits on a rotating stoll holding two 8.0kg objects. When his arms are extended horizontally, the objects are 1.3m from the axis rotation and he rotated with an angular speed of 1.8rad/s. The moment of intertidal of the student plus stoll is 4.5kg•m^2 and is assumed to be constant.  if the student pulls in the two objects horizontally to 0.50m from the rotation axis. What is the new angular speed in rad/s of the student? (3 sig fig)

In a popular amusement park ride, a rotating cylinder of radius R = 3.10 m is set in rotation at an angular speed of 5.30 rad/s, The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider's clothing and the wall is needed to keep the rider from slipping?