At a certain instant a rigid wheel is spinning about its center of mass with angular velocity of magnitude w and angular acceleration of magnitude a. Consider a point a distance r from the axis of rotation. U
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- A 3.0-kg mass slides on a frictionless horizontal surface with a speed of 3.0 m / s when it collides with a 1.0-kg mass initially at rest as shown in the figure. The two masses stick to each other and slide on a frictionless circular wheel portion of radius 0.40 m. At what maximum height h, above the horizontal, do the masses reach? Answers: a) 0.18 m b) 0.15 m c) 0.21 m d) 0.26 m e) 0.40 mA kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ω. Assume that the kid has a mass of 40 kg and is initially running at a speed of 2 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 120 kg and a radius of 2 m. Assume that it rotates without friction. What is the final angular velocity ωf (in radians/s) of the merry-go-round (with the kid riding)? Please write out steps, not type-I have dyslexiaA kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ω. Assume that the kid has a mass of 40 kg and is initially running at a speed of 4 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 80 kg and a radius of 2 m. Assume that it rotates without friction. What is the final angular velocity ωf (in radians/s) of the merry-go-round (with the kid riding)?
- W; = 0 %3D Wf initial final A flywheel consists of a thin uniform disk of mass m and radius R, free to rotate about a frictionless central axle. A small weight, also of mass m, is attached to the wheel's rim. The is wheel is held at rest (left), the small weight level with the axle, then released. What is the angular velocity of the wheel when the weight reaches its lowest point? 4g V 3R 8g V 5R 3g V 2R V28R 2gRA solid disk with radius r= 1Ocm rolls smoothly from rest from the top of the roof that is 12m long and inclined 30°. Using energy conservation law, calculate a) the velocity of the center of mass of the disk at the edge, b) the angular velocity of the disk at the same moment. The moment of inertia of a solid disk rotated about its center is I=1/2MR?A light rigid bar of length, l = 1m, is attached to two particles, with masses m1 = 4 kg and m2 = 3 kg, at their ends. The combination rotates in the xy plane about an axis through the center of the bar, right figure. Determine the angular momentum of the system about the origin when the speed of each particle is 5 m / s.
- How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.0 cm and a mass of 15.8 g. The laser scans at a constant tangential velocity of 1.20 m/s. Assume that the music is first detected at a radius of 29.0 mm from the center of the disk. Ignore the small circular hole at the CD’s center. in JA solid cylinder (disk) and a hollow cylinder are rolling with the same center- of-mass velocity v = 2 m/s on a level surface towards an incline. Both R cylinders have the same radius R and mass M. The moments of inertia are: 1 Solid cylinder 1, MR² Hollow cylinder I, = MR² (a) What is true about the kinetic energy when the cylinders are rolling on level ground? (i) they have the same translational kinetic energy (ii) they have the same rotational kinetic energy (iii) they have the same total kinetic energy [1] only (i) [2] only (ii) [3] (i) and (ii) [4] (i) and (iii) [5] (i), (ii), and (iii) (b) Which conservation law will allow you to calculate the final height? Conservation of: [1] momentum [5] moment of inertia [2] mechanical energy [3] kinetic energy [4] angular momentum (c) Calculate the maximum height the solid cylinder will reach before it rolls down again; please use g = 10 m/s². (d) Calculate the maximum height the hollow cylinder will reach before it rolls down again.Plz asap
- A uniform horizontal disk of radius 5.50 m turns without friction at w = 2.30 rev/s on a vertical axis through its center, as in the figure below. A feedback mechanism senses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant while a m = 1.20 kg block on top of the disk slides outward in a radial slot. The block starts at the center of the disk at time t = 0 and moves outward with constant speed v = 1.25 cm/s relative to the disk until it reaches the edge at t = 465 s. The sliding block experiences no friction. Its motion is constrained to have constant radial speed by a brake at B, producing tension in a light string tied to the block. (a) Find the torque as a function of time that the drive motor must provide while the block is sliding. Hint: The torque is given by = 2mrvw. t N-m (b) Find the value of this torque at t= 465 s, just before the sliding block finishes its motion. N.m 2.52 (c) Find the power which the drive motor must…In the figure, the disk is at rest, homogeneous, and weighs 50 lb. If a horizontal force P is applied to its center of mass at G, and it experiences friction as shown, determine the angular acceleration of the disk and the acceleration of point G.