Two are balls situated one on top of the other and the lower one is fixed to the ground. The ball on top rolls down the lower one without slipping and falls off. What is the angle 0 at which the two balls loose contact? Both balls are of mass m and radius R.
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- A 98.3 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.79 rad/s. A monkey drops a 8.13 kg bunch of bananas vertically onto the platform. They hit the platform at 45 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 22.1 kg, drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.95 m.A 1000 kg car moves with a speed of 50 m/s on a circular track of radius 100 m. What is the magnitude of its angular momentum (in kg m2/s) relative to the center of the race track?A hamster is sprinting around a circular track. It is sprinting at a speed of 4 meters per second. The hamsters mass is 1.2kg, the radius of the circular track is 234 meters. What is the angular momentium?
- A 10-g, 7.0-cm-long spinner on a numbers wheel in a board game is fastened 1.0 cm from one of its ends. The spinner is then set in motion with an angular velocity of 50 rad/s as it spins about its fastened end. What is the angular momentum of the spinner relative to the given axis of rotation?You are standing on a cylindrical raft, which is floating on water. Initially the raft together with you is rotating with angular velocity =0.1 s-¹ . Then you start running along the periphery in order stop the rotation of the raft. How fast and in what direction should you run? Your mass is 75 kg, the raft has mass 200 kg and its radius is 15 m.A 88.3 kg88.3 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.77 rad/s1.77 rad/s. A monkey drops a 9.71 kg9.71 kg bunch of bananas vertically onto the platform. They hit the platform at 4545 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 21.7 kg21.7 kg, drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.65 m1.65 m.
- A merry-go-round is a common piece of playground equipment. A 3.0-mm-diameter merry-go-round, which can be modeled as a disk with a mass of 260 kgkg , is spinning at 17 rpmrpm. John runs tangent to the merry-go-round at 5.4 m/sm/s, in the same direction that it is turning, and jumps onto the outer edge. John's mass is 30 kgkg. Part A What is the merry-go-round's angular velocity, in rpmrpm, after John jumps on? Express your answer in revolutions per minute.A disk of mass m₂ = 70.0 g and radius ₁ = 4.50 cm slides on a frictionless sheet of ice with velocity v, where v = 13.00 m/s, as shown in a top-down view in figure (a) below. The edge of this disk just grazes the edge of a second disk in a glancing blow. The second disk has a mass m₂ = 140 g, a radius r₂ = 6.00 cm, and is initially at rest. As the disks make contact, they stick together due to highly adhesive glue on the edge of each, and then rotate after the collision as shown in figure (b). my 11₂ a (a) What is the magnitude of the angular momentum (in kg m²/s) of the two-disk system relative to its center of mass 3.28E-3 x kg m²/s (b) What is the angular speed (in rad/s) about the center of mass? 70.5 X rad/sParalel axis theorem) = 0.108m Isaいd ニ Sphere MR? しR-0.1og。 A bowling ball of mass 7.1 kg and diameter 21.6 am is thrown down the alley at a speed of 8.7 m/s. The bowling ball is initially skidding, with no angular velocity, down the alley. The coefficient of friction between the ball and the alley is (0.30, 0.25). Motion Information Event 1:1 Free-Body Diagram Event 2: re byl! t, =0 12 = いitroa* Sipi. 12 = 02 = 0, = V; = 8,7mls 01 = 0 V2 = 02 = aj = KF az = a2 = aj = Mathematical Analysis V½ =WqRt Cond,i tionof event 2 untilthen, The FBD aboveis vali?, and ball AiCcedernting 2 EF=- "F = Mamg = ma> a= -Meg * MR G: EF:0 :f - mg F:mg a £ Roc 5 MM g %3D %3D => 2 R Calculate %3D Vz = V, + a€z the rest is easy Solve for te...A puck of mass m = 1.10 kg slides in a circle of radius r = 19.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 2.20 kg by a cord through a hole in the table. What speed keeps the cylinder at rest? m/sA horizontal circular platform rotates counterclockwise about its axis at the rate of 0.827 rad/s. You, with a mass of 74.5 kg,walk clockwise around the platform along its edge at the speed of 1.13 m/s with respect to the platform. Your 20.5 kg poodle also walks clockwise around the platform, but along a circle at half the platform's radius and at half your linear speed with respect to the platform. Your 18.7 kg mutt, on the other hand, sits still on the platform at a position that is 3/4 of the platform's radius from the center. Model the platform as a uniform disk with mass 90.9 kg and radius 1.87 m. Calculate the total angular momentum of the system.A 93.7 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.55 rad/s. A monkey drops a 9.75 kg bunch of bananas vertically onto the platform. They hit the platform at of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 21.3 kg, drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.95 m. angular velocity: rad/sSEE MORE QUESTIONS