The motion of spinning a hula hoop around one's hips can be modeled as a hoop rotating around an axis not through the center, but offset from the center by an amount h, where h is less than R, the radius of the hoop. Suppose Maria spins a hula hoop with a mass of 0.74 kg and a radius of 0.67 m around her waist. The rotation axis is perpendicular to the plane of the hoop, but approximately 0.45 m from the center of the hoop. (a) What is the rotational inertia of the hoop in this case? kg · m2 (b) If the hula hoop is rotating with an angular speed of 13.3 rad/s, what is its rotational kinetic energy? J

Your roommate is working on his bicycle and has the bike upside down. He spins the 56.0 cmcm -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What is the pebble's acceleration? Express your answer with the appropriate units.   The answer is NOT 110 49.7 49.8 or 0.63

A 33.2 kg boy and a 22.0 kg girl are standing at the edge of a 161 kg merry-go-round of radius 1.41 m that is currently rotating at 32.0 rpm. The two kids then walk inward toward the center of the merry-go-round; while the boy reaches the center, the girl stops halfway. Given their new positions, what is the new rate of rotation of the merry-go-round (in rpm)? For simplicity's sake, you may treat the kids as point masses and the merry-go-round as a flat disk. Hint: Figure 10.12 in the textbook provides a good refresher on the various moments of inertia!

A rock tied to the end of string swings at a constant angular rate. If you are told that the string can support a total of 85 N of force before breaking, what is the maximum angular velocity the rock can rotate if the rock has a mass of 0.16 kg, and the length of the string is 0.5 m? Give your answer in units of radian per second

1. The horizontal circular platform weighs 500 lb and has a radius of gyration of kz = 8 ft from the z-axis passing through O. The platform is free to rotate about the z-axis and is initially at rest. A person having a weight of 150 lb begins to run along the edge in a circular path of radius 10 ft. If they maintain a speed of 4 ft/s relative to the platform, determine the angular velocity of the 10 ft platform. Neglect friction. I don't think we have dealt with relative velocity in this context, but it follows our earlier relative velocity treatment. Here all speeds are in the t-direction. vp is the speed of the person, and vp is the speed of the disk at the location of the person. Then vp = vp + Vp/D, same as before. You are given vpp = 4 ft/s.

Problem 5: A ball with a mass of 0.220kg is connected to a string with a length of 1.20m long so that the ball undergoes uniform circular motion with constant speed. If the string exerts a force of 30.0N to keep the ball rotating, a) what is the speed of the ball? b) What is the angular speed of the ball? (10 points)

A 170-kg merry-go-round of radius 2.10 m is rotated by pulling a rope that is wrapped around its edge. What is the magnitude of the force (assume it to be constant) on the rope needed to bring the merry- go-round from rest to an angular speed of 0.400 rev/s in 3.00 s? (The moment of inertia of merry-go- round is 1/2MR2).

A small block on a frictionless, horizontal surface has a mass of 2.30x10-2 kg. It is attached to a massless cord passing through a hole in the surface (Figure 1). The block is originally revolving at a distance of 0.300 m from the hole with an angular speed of 2.87 rad/s. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.150 m. Model the block as a particle. Figure ▼ Express your answer with the appropriate units. AK = 2.8210-² Part D μA W = Submit Previous Answers Request Answer Submit 3 X Incorrect; Try Again; 3 attempts remaining → How much work was done in pulling the cord? Express your answer with the appropriate units. HÅ -0.0123 Provide Feedback J PHO ? J 0 PE ? Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining Constants Next >

A uniform disk of radius R is free to rotate about its central axis. A mass m is hung vertically from the disk at a distance 2/5 R from the axis. R 2R/5 m What is the magnitude of the force F (the solid-lined arrow in the figure) which must be applied to prevent the disk from rotating? Omg O 3mg/5 O2mg/5 O 5mg/2

Two big bugs, Buzz and Crunchy each of mass 0.65 kg, are siting on a spinning disk on a horizontal plane. Buzz is sitting halfway and Crunchy is sitting at the outer edge as shown. The radius of the disk is 9.5 m and it rotates once every 1.2 s. What is the magnitude of the net force on Buzz, in Newtons?