4. A hoop is thrown onto the ground without bouncing. Initially the velocity of the center of the hoop is to the right at 2 m/s, and it has a backspin of 5 rad/s. What will be the speed and direction of the center of the hoop when it stops slipping relative to the ground? State 1 m = 0.75 kg R = 0.5 m State 2 w₁ = 5 rad/s V₁ = 2 m/s v₂ =? slipping rolling without slipping
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- A solid uniform spherical boulder travels down a hill. At the top of the hill the boulder is rolling with a horizontal speed of 5 m/s. The top half of the hill is rough, so that the boulder continues to roll without slipping. The bottom half of the hill and the valley is covered in smooth ice, so that there is no static friction between the boulder and the hill. How fast is the boulder moving when it gets to the bottom of the hill? What is its rotational speed in the valley if the boulder has a radius of 10 cm? Rough 50.0 m SmoothÏ A disc (thin cylinder) of mass 0.29 kg and radius 0.75 m is rotating on a frictionless axle at a constant rate of 82 RPM. What is the moment of inertia for this disc? kg.m² A second disc of 0.14 kg and 0.41 m is dropped down the axle on top. The two then rotate together. What is the final moment of inertia for both discs together? kg/m² |=| |=A system of point particles is shown in the following figure. Each particle has mass 0.43 kg, and they all lie in the same plane. 62 cm 49 cm axis 29 cm (a) What is the moment of inertia (in kg. m²) of the system about the given axis? kg-m² (b) If the system rotates at 5.6 rev/s, what is its rotational kinetic energy (in J)? J
- 6. A merry-go-round has a moment of inertia I = 740.0 kg-m² and radius of 2.30m. A child with m = 34.0kg runs at the merry-go-round (MGR) at v = 2.60m/s. His straight line path would miss the center of the MGR by a distance of 1.30m. What is his angular momentum relative to the MGR center before reaching it? If the MGR is initially at rest, what is its angular speed after the child jumps on assuming the child stays at the outer rim? R mA disk of radius R, mass M, and moment of inertia I = (1/2)MR- rolls without slipping down an incline and onto a horizontal table. The disk then continues to the right and goes up a frictionless ramp. The disk starts at rest at a height h above the table, as shown . What is the speed of the center of mass of the disk when it reaches the bottom of the ramp? O A. V1/2gh OB. V5/3gh OC. 4/3 gh OD. 6/7gh O E. None of the aboveA disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In what order do they reach the bottom? sphere, hoop, disk O disk, hoop, sphere O sphere, disk, hoop O hoop, sphere, disk O hoop, disk, sphere