R Figure P7.27

A tire is tied to a rope that is tied to the branch of a tree so that the tire swings in a circular trajectory of radius h1 = 15.31 m. A child takes the tire to the top of a platform that is a height h2 = 12.60 m above the ground, sits in the tire, and swings from rest from the platform. The combined mass of the tire and child is 36 kg. The rope is taut when the child leaves the platform and you may neglect the mass of the rope. At the bottom of the circular trajectory, the child and tire are a height h3 = 0.99 m above the ground. include a diagram showing the physical sites (a) Calculate the speed of the child/tire at the bottom of the circular trajectory.  m/s (b) Calculate the maximum tension in the rope as the child/tire swing back and forth.  N

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.

A child's top is held in place upright on a frictionless surface. The axle has a radius of r 3.21 mm. Two strings are wrapped around the axle, and the top is set spinning by T T applying T = 2.40 N of constant tension to each string. If it takes 0.590 s for the string to unwind, how much angular 2r momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. R SP 9.15 x10¬3 kg-m² L = S Point P is located on the outer surface of the top, a distance h = 35.0 mm above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is 0 = 24.0°. If the final tangential speed v, of point P is 1.45 m/s, what is the top's moment of inertia I? T 2r T 2.42 x10-4 kg-m? = Incorrect

A playground merry-go-round of radius 4m has a moment of inertia of 324 kg m² and is rotating at 11 rev/min about a frictionless vertical axle. Facing the axle, a 25.0 kg child hops on and manages to sit down on the edge. What is the new rotational speed of the merry-go-round in rev/min?

A 250 g piece of kryptonite is attached to a 90 cm long masless string to form a pendulum. At its highest point (Point A) the string makes an angle of 55 degrees with the vertical. Its lowest point is Point B and Point C is where the string makes an angle of 35 degrees with respect to the vertical. Find the tension in the string and angular acceleration of the rock at (a) Point A, (b) Point B and (c) Point C.  (a) Draw a free body diagran of the kryptonite, including all relevant angles and axes at Point A, Point B, and Point C. (Three total FBD) (b) Find the angular speed, angular acceleration and tension in the string at Point A.  (c) Find the angular speed, angular acceleration, centripetal force and tension in the string at Point B. (d) Find the angular speed, angular acceleration, centripetal force and tension in the string at Point C.

An air puck of mass 0.30 kg is tied to a string and allowed to revolve in a circle of radius 1.3 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.5 kg is tied to it. The suspended mass remains in equilibrium while the puck on the tabletop revolves. (a) What is the tension in the string? N (b) What is the force causing the centripetal acceleration on the puck? (c) What is the speed of the puck? m/s Need Help? Read It

A massless, frictionless merry-go-round of radius R has one child of mass M sitting on the outer edge and is spinning with angular velocity ωi. If the child walks towards the center until she is 0.50R from the center, by what factor does the angular velocity increase? (i.e. solve for F where ωf=Fωi)

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?