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- A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a radius R = 1.5 meters, and a mass M = 251 kg. A small boy of mass m = 41 kg runs tangentially to the merry-go-round at a speed of v = 1.8 m/s, and jumps on.Randomized VariablesR = 1.5 metersM = 251 kgm = 41 kgv = 1.8 m/s (a) Calculate the moment of inertia of the merry-go-round, in kg ⋅ m2. Part (b) Immediately before the boy jumps on the merry go round, calculate his angular speed (in radians/second) about the central axis of the merry-go-round.(c) Immediately after the boy jumps on the merry go round, calculate the angular speed in radians/second of the merry-go-round and boy.(d) The boy then crawls towards the center of the merry-go-round along a radius. What is the angular speed in radians/second of the merry-go-round when the boy is half way between the edge and the center of the merry go round?(e) The…A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a radius R = 1.3 meters, and a mass M = 251 kg. A small boy of mass m = 42 kg runs tangentially to the merry-go-round at a speed of v = 1.2 m/s, and jumps on. Randomized Variables R = 1.3 metersM = 251 kgm = 42 kgv = 1.2 m/s a)Calculate the moment of inertia of the merry-go-round, in kg ⋅ m2. b) Immediately before the boy jumps on the merry go round, calculate his angular speed (in radians/second) about the central axis of the merry-go-round. c) Immediately after the boy jumps on the merry go round, calculate the angular speed in radians/second of the merry-go-round and boy.A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a radius R = 1.3 meters, and a mass M = 251 kg. A small boy of mass m = 42 kg runs tangentially to the merry-go-round at a speed of v = 1.2 m/s, and jumps on. Randomized Variables R = 1.3 metersM = 251 kgm = 42 kgv = 1.2 m/s a) The boy then crawls towards the center of the merry-go-round along a radius. What is the angular speed in radians/second of the merry-go-round when the boy is half way between the edge and the center of the merry go round? b) The boy then crawls to the center of the merry-go-round. What is the angular speed in radians/second of the merry-go-round when the boy is at the center of the merry go round? c)Finally, the boy decides that he has had enough fun. He decides to crawl to the outer edge of the merry-go-round and jump off. Somehow, he manages to jump in such a way that he hits the…
- Note: Because the arguments of the trigonometric functions are unitless in this question, your calculator must be in radian mode if you use it to evaluate any trigonometric functions. When powered up, a disk drive starts at rest and spins up with non-uniform angular acceleration according to the following formula: =asin(bt) where a = 708 radians/s2 and b = 1.74 s-1. This lasts for the first 1.81 seconds, after which the drive does not accelerate. How many meters of disk surface have passed underneath the head in 0.79 seconds?In an experiment where we will use a vertically-mounted turntable that has a hub attached at its center, which has three grooves of different radius, around which one can wind a string. A mass hanging from the free end of the string provides tension, which exerts a torque on the turntable, thus causing it to rotate What effect does the diameter of the string have on the lever arm? Explain why we can ignore this effect. Please help guide me as to what the string's diameter's effect is on the lever arm, and why this effect can be ignored.The angular moomentum of a point with a mass of m, a velocity v, and position r is: L = mr x v. Prove that the rate of change of L, dL/dt is equal to the torque (T = r x F). F is the force on the point.
- A single bead can slide with negligible friction on a stiff wire that has been bent into a circular loop of radius 15.0 cm as shown. The circle is always in a vertical plane and rotates steadily about its vertical diameter with a period of 0.450 s. The position of the bead is described by the angle θ that the radial line, from the center of the loop to the bead, makes with the vertical. (a) At what angle up from the bottom of the circle can the bead stay motionless relative to the turning circle? (b) What If? Repeat the problem, this time taking the period of the circle’s rotation as 0.850 s. (c) Describe how the solution to part (b) is different from the solution to part (a). (d) For any period or loop size, is there always an angle at which the bead can stand still relative to the loop? (e) Are there ever more than two angles? Arnold Arons suggested the idea for this problem.A uniform sphere of mass m and radius R rolls without slipping down a plane at an angle θ from thehorizontal. Show that the acceleration along the slope of the center of mass is aCM = (5/7)g sin θ and that the force of static friction needed is fs = (2/7)mg sin θ. What minimum coefcient of friction µs is needed to satisfythe conditions of the problem?Answer D, E, & F: Given that a) M*Vd b) M*V^2 C) M*Vd ( angular momentum is conserved)
- If small particle 'm' is placed a distance 'x' from the central axis of a solid disk of total mass M with 'r' radius, what would the be force?I don't understand why B would be the correct answer? Shouldn't the potential energy be decreasing as Mars gets farther, since the gravitational force decreases? And why is angular momentum the same?A uniform rod of mass 190 g and length 100 cm is free to rotate in a horizontal plane around a fixed vertical axis through its center, perpendicular to its length. Two small beads, each of mass 24 g, are mounted in grooves along the rod. Initially, the two beads are held by catches on opposite sides of the rod's center, 12 cm from the axis of rotation. With the beads in this position, the rod is rotating with an angular velocity of 15.0 rad/s. When the catches are released, the beads slide outward along the rod. (a)What is the rod's angular velocity (in rad/s) when the beads reach the ends of the rod? (Indicate the direction with the sign of your answer.) _______ rad/s (b)What is the rod's angular velocity (in rad/s) if the beads fly off the rod? (Indicate the direction with the sign of your answer.) ________rad/s