10.1 Rotational Variables

29. A track star runs a 4DDm race on a 4DDm circular track in 45 s. What is his angular velocity assuming a constant speed? 31. A particle moves 3J3 m along a circle of radius 1.5 m. {a} Through what angle does it rotate? lb} if the particle makes this trip in 1.0 s at a constant speed, what is its angular velocity? {c} What is its acceleration? 33. Unreasonable results. The propeller of an aircraft is spinning at 10' rows when the pilot shuts off the engine. The propeller reduces its angular velocity at a constant 2.1] Haifa2 for a time period of 46 s. What is the rotation rate of the propeller in 413 s'? Is this a reasonable situation? 10.2 Rotation with Constant Angular Acceleration 37. A wheel has a constant angular acceleration of 5.0 rad/s . Starting from rest, it turns through 300 rad. (a) What is its final angular velocity? (b) How much time elapses while it turns through the 300 radians?43. A circular disk of radius 10 cm has a constant angular acceleration of 1.0 rad/s'; at t = 0 its angular velocity is 2.0 rad/s. (a) Determine the disk's angular velocity at t = 5.0 s. (b) What is the angle it has rotated through during this time? (c) What is the tangential acceleration of a point on the disk at t = 5.0 s?51. A child with mass 40 kg sits on the edge of a merry-go-round at a distance of 3.0 m from its axis of rotation. The merry-go-round accelerates from rest up to 0.4 rev/s in 10 s. If the coefficient of static friction between the child and the surface of the merry-go-round is 0.6, does the child fall off before 5 s?55. (a) Calculate the rotational kinetic energy of Earth on its axis. (b) What is the rotational kinetic energy of Earth in its orbit around the Sun?61A system consists of a disk of mass 2.0 kg and radius 50 cm upon which is mounted an annular cylinder of mass 1J2) kg with inner radius 20 cm and outer radius 30 cm {see below}. The system rotates about an axis through the center of the disk and annular cylinder at 10 rew's. {a} What is the moment of inertia of the system? (b) What is its rotational kinetic energy? 50 cm 30 cm 20 cm