A hoop of mass M = 3 kg and radius R = 0.4 m rolls without slipping down a hill, as shown in the figure. The lack of slipping means that when the center of mass of the hoop has speed v, the tangential speed of the hoop relative to the center of mass is also equal to vCM, since in that case the instantaneous speed is zero for the part of the hoop that is in contact with the...
A string is attached to the rim of a small hoop of radius r= 8.00×10−2 m and mass m = 0.180 kg and then wrapped several times around the rim. If the free end of the string is held in place and the hoop is released from rest and allowed to drop, as shown in the figure (Figure 1) , calculate the angular speed and the translational speed of the rotating hoop after it has descended h = 0.750 m...
4. The figure below shows a hoop with mass m = 0.5 kg and radius a at rest on a frictionless table. Right a disk with mass M = 2m and radius b spinning with angular velocity W = 5.0 rad/s, and it is dropped onto the hoop. Eventually, the hoop and the disk rotate together with angular velocity 0. a. What is w? Express it in terms of a and b. (12 pts) b. How much energy AE is...
A hoop of mass M = 2 kg and radius R = 0.4 m rolls without slipping down a hill, as shown in the figure. The lack of slipping means that when the center of mass of the hoop has speed v, the tangential speed of the hoop relative to the center of mass is also equal to VCM, since in that case the instantaneous speed is zero for the part of the hoop that is in contact with the...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 3.5 s. If R = 1.2 m and m = 3.3 kg, calculate the angular momentum about that axis.
A thin stick of mass 0.5 kg and length L = 0.8 m is attached to the rim of a metal disk of mass M = 5.0 kg and radius R = 0.4 m. The stick is free to rotate around a horizontal axis through its other end (see the following figure). (a) If the combination is released with the stick horizontal, what is the speed (in m/s) of the center of the disk when the stick is vertical? m/s...
A uniform disk with mass 38.8 kg and radius 0.200 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 25.0 N is applied tangent to the rim of the disk. a)What is the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.170 revolution? b)What is the magnitude a of the resultant...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length Rand mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 2.1 s. If R=0.9 m and m-4.0 kg, calculate the angular momentum about that axis. Number i Units
A thin hoop of radius r = 0.82 m and mass M = 7.3 kg rolls without slipping across a horizontal floor with a velocity v = 1.1 m/s. It then rolls up an incline with an angle of inclination theta = 44 degrees. a) What is the maximum height h reached by the hoop before rolling back down the incline? b) Now, suppose a uniform solid sphere is used instead of a hoop. Use the same values of r,...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length Rand mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 3.5 s. If R = 1.2 m and m = 3.3 kg, calculate the angular momentum about that axis. Rotation axis Number Units