(a) What is the final velocity, in m/s, of a hoop that rolls without slipping down a 5.00 m high hill, starting from rest? m/s (b) What would be the final velocity, in m/s, if a uniform solid disk of the same mass and radius as the hoop rolled down the hill? m/s
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- A solid cylinder with radius, R, mass, M and length, L is fixed to rotate on its cylindrical axis. A string with negligible mass wound around the cylinder and pulled with force, F. What is the linear acceleration of a point on the outer circumference of the cylinder?A 200kg disk with a radius of 4.0m is rotating clockwise about the +y axis. A 50kg person is sitting 2.5m from the rotational axis. a) What is the total moment of inertia of the disk and person together? b) What is the initial angular momentum Li of the system? c) A constant 30.0N force is applied to the edge of the disk with an angle of 60° with respect to the moment arm. (+y out of page in top down view) What is the torque on the system? d) What is the final angular momentum if the torque is applied for 2s?A turnable with a moment of interia of 0.012 kg m² rotates freely at 2.0 rad/s. A circular disk of mass 200 g and diameter 30 cm, and initially not råtating, slips down a spindle and land on the turnable. (A) Find the new angular speed. (B.) Whot is the change in kinetic energy?
- A uniform solid ball rolls without slipping down a plane which is inclined at 31° to the horizontal. If the ball has a radius r=0.4m, a mass m=0.1 kg and starts from rest, find: a) the speed of the ball after it travels 2m down the incline. b) at this point, what is the angular momentum of the ball? c) If the coefficient of friction between the ball and the plane is 0.25, what is the maximum angle of inclination that allows the ball to roll without slipping?A playground merry-go-round (a solid disk) has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 22.0-kg child (who is initially at rest) gets onto it by grabbing its outer edge? (You can approximate the child as a point mass). (Hint: here you'll need to use the conservation of angular momentum.) a. 0.683 rev/s b. 0.415 rev/s c. 0.366 rev/s d. 0.129 rev/sA 20-kg child running at 1.4 m/s jumps onto a playground merry-go-round that has mass 180 kg and radius 1.6m. She is moving tangent to the platform when she jumps and she lands right on the edge. What is the angular velocity of the child and the merry-go-round if the merry-go-round started from rest? You can treat the merry-go-round as a solid disc and ignore any friction in its axle. Please answer in units of rad/sec.
- A string is wrapped around a pulley of radius 1 m and moment of intertia 5 kgm2. If the string is piulled with a force F, the resulting angular acceleration of the pulley is 5o rad/s2 . Determine the magnitude of the force F.A thin, 20-gram hoop with a radius of 2 meters is rolling without slipping, initially along a level surface, with its center of mass moving at 20 m/s and with a rotation rate about that center of mass of 10 rad/s. Then it rolls up an incline, coming to rest (momentarily) as shown below. В Vcm =0 m/s Wcm=0 rad/s Wcm=10rad/s h Vcm = 10m/s A Below is the work-energy equation with all the forms of energy we have discussed up to now. Which of these energy terms are zero? ΔΕhem+ΔΚΕ+ ΑΚΕΡ+ Δυ Δυ ΔΕ ound ΔΕ Wext(a) What is the final velocity, in m/s, of a hoop that rolls without slipping down a 7.10 m high hill, starting from rest? m/s (b) What would be the final velocity, in m/s, if a disk of the same mass and radius as the hoop rolled down the hill? m/s