F2

A solid cylinder is mounted above the ground with its axis of rotation oriented horizontally. A rope is wound around the cylinder and its free end is attached to a block of mass 55.0 kg that rests on a platform. The cylinder has a mass of 255 kg and a radius of 0.490 m. Assume that the cylinder can rotate about its axis without any friction and the rope is of negligible mass. The platform is suddenly removed from under the block. The block falls down toward the ground and as it does so, it causes the rope to unwind and the cylinder to rotate. (a) What is the angular acceleration, in rad/s², of the cylinder? rad/s2 (b) How many revolutions does the cylinder make in 5 s? rev (c) How much of the rope, in meters, unwinds in this time interval?

A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg · m2 and is rotating at 10.0 rev/min about a frictionless, vertical axle. Facing the axle, a 25.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round?

A thin rod has a length of 0.900 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.607 rad/s and a moment of inertia of 1.06 x 10-3 kg-m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod? Number i Units

During the spin cycle the time dependent angular speed of a washing machine drum is given by the equation ω(t) = at + bt2 - ct4 where a = 1.1 rad/s2, b = 0.65 rad/s3 and c = 0.035 rad/s5. At time t = 0 s, a point P on the washer drum is located at θ0 = 1.8 rad. Part (a)  Write an equation for the angular acceleration of the drum, as a function of time, in terms of the given parameters.  Part (b)  What is the angular acceleration, in radians per square second, at time t = 2.2 s?   Part (c)  Write an equation for the angular position of the point P, as a function of time, in terms of the given parameters.    Part (d)  What is the angular position of the point P on the drum, in radians, at t = 2.2 s?

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

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?

A carousel has a radius of 1.60 m and a moment of inertia of 130 kg · m2.A girl of mass 43.0 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.10 rad/s. Now the girl walks toward the center of the carousel and stops at a certain distance from the center d. The angular speed of the carousel is now 5.4 rad/s. How far from the center, in meters, did the girl stop?