A ball of mass 0.320 kg is attached to one end of a light inextensible string of length 0.600 m, whose other end is attached to a fixed pivot. The ball performs uniform circular motion in a horizontal plane, with the string making an angle of 30.0° with the vertical. What is the angular speed of this circular motion?

In testing an automobile tire for proper alignment, a technician marks a spot on the tire 0.230 m from the center. He then mounts the tire in a vertical plane and notes that the radius vector to the spot is at an angle of 33.0° with the horizontal. Starting from rest, the tire is spun rapidly with a constant angular acceleration of 1.60 rad/s2.(Assume the spot's position is initially positive, and assume the angular acceleration is in the positive direction.) (a) What is the angular speed of the wheel after 1.20 s? rad/s (b) What is the tangential speed of the spot after 1.20 s? m/s (c) What is the magnitude of the total acceleration of the spot after 1.20 s? m/s2 (d) What is the angular position of the spot after 1.20 s?

A solid disk of uniform density and mass M = 0.950 kg with radius R = 0.250 m is suspended vertically and is free to rotate about its center without friction. A point object that has the same mass as the disk is placed at an angle 0 = 25.0° clockwise from the top along the rim, causing the disk to rotate. The acceleration due to gravity is g=9.81m/s². What is the angular speed wf of the disk when the point object is directly below the center of the disk? R 0.

A 5 kg ball with a 0.4 meter radius is rolling on a horizontal surface at 3 m/s. The rotational inertia of the ball is 0.4mr2. The ball rolls up a 30-degree inclined plane. What is the maximum height that the ball reaches?

Two girls (26 kg each) are standing on the edge of a solid, rotating disk of mass 70 kg and radius 1.3m. The initial angular speed of the disk is 0.71 rev/s. If one of the girls moves slowly toward the center while the other stays put at the edge, what is the new angular speed of the disk when she reaches the halfway point?

A small 0.360-kg object moves on a frictionless horizontal table in a circular path of radius 3.00 m. The angular speed is 4.97 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 160 N, what is the radius of the smallest possible circle on which the object can move?

A Texas cockroach walks from the center of a circular disk (that rotates like a merry-go-round without external torques) out to the edge at radius R. The angular speed of the cockroach–disk system for the walk is (va = 5.0 rad/s and vb = 6.0 rad/s). After reaching R, what fraction of the rotational inertia of the disk does the cockroach have?

A spinning globe is slowed at a constant acceleration of 0.750 rad/s2 until it stops. One of the points on the equator moves 23.0° in the first 0.700 s of the slowing phase. (a) Find the total angular displacement of the globe during the acceleration phase. (b) Find the initial angular speed of the globe.

Point A of the circular disk is at the angular position 0 = 0 at time t = 0. The disk has angular velocity wo = 0.29 rad/s at t = 0 and subsequently experiences an angular acceleration a = 1.8t where t is in seconds, and a is in radians per second squared. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 2.7 s. Assumer = 145 mm. α Answers: VA = aд = 90 (i ( i 0 6.806 i + i + i i 1 0.705 j) m/s j) m/s²

A cylinder has a cone removed from it.  The cylinder and the conical hole have the same radius (2.06 meters) and height (4.56 meters).  The cylinder has a density of 447 kg/m3. What is the rotational inertia of the cylinder with the cone removed in kg m2?  You can set your origin at the tip of the cone, which is also the center of the base of the cylinder.