Use the concepts of angular momentum and conservation of angular momentum to explain why it is easier to stay balanced on a bicycle when it is moving as opposed to when it is at rest. In your response, be sure to mention the direction of the angular momentum vector.
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- A 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 dyslexiaI was wondering if I could have some guidance on a homework question. I was unable to find help, so I would just like some tips that point me in the right direction. Here is some background info: Setup For our dynamic measurement of the moment of inertia, 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. By measuring the time it takes the mass to fall from its initial height to the table top (or some reference line just above it), we can find aa, its (linear) acceleration. From this we can calculate αα, the angular acceleration of the turntable. From the weight of the mass, and its linear acceleration, we can find T, the tension in the string. Once we know all these things, we can calculate the torque, ττ, and from τ=Iατ=Iα find I, the moment of…(hrw8c11p74) A uniform rod rotates in a horizontal plane about a vertical axis through one end. The rod is 16.00 m long, weighs 26.67 N, and rotates at 250 rpm clockwise when seen from above. Calculate the rotational inertia of the rod about the axis of rotation, then calculate the angular momentum of the rod about that axis.
- Suppose that in the example with Joey and the toy airplane, he pulls the airplane closer to him. Initially, the length of the string is a and after he pulls it closer, it’s a/4. In this case, there is no torque acting on the airplane (the angle between the force exerted by Joey and the vector is 180°, so the torque is zero), thus, the angular momentum of the airplane is conserved. Your goal is to determine the new speed of the airplane after Joey pulls it closer, assuming that initially, its speed was vi. What is the initial angular momentum (magnitude) of the airplane? What is the final angular momentum (magnitude) of the airplane? (Use as its final speed) What is the final speed of the airplane?Two astronauts, each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, moving in circles around the point halfway between them at speed v. c) By pulling on the rope, the astronauts shorten the distance between them to d/2. What is the new angular momentum of the system?d) What are their new speeds?e) What is the new rotational energy of the system?f) How much work is done by the astronauts in shortening the rope?A bicycle wheel, of mass 1.52 kg is placed at the end of a rod 0.630 m in length, which can pivot freely about the other end. D- The rod is of negligble mass. The wheel is turning rapidly such that it has an angular momentum of 15.1 kgm2/s. At what angular speed does the wheel revolve horizontally about the pivot? Submit Answer Tries 0/10
- How do you solve this?A disk slides toward a motionless stick on a frictionless surface (figure below). The disk strikes and adheres to the stick and they rotate together, pivoting around the nail. Angular momentum is conserved for this inelastic collision because the surface is frictionless and the unbalanced external force at the nail exerts no torque. Before M Nail (pivot) (b) What is the kinetic energy (in J) before and after the collision? J K before K J after (b) Consider a situation where the disk has a mass of 52.5 g and an initial velocity of 32.5 m/s when it strikes the stick that is 1.30 m long and 2.20 kg at a distance of 0.100 m from the nail. (a) What is the angular velocity (in rad/s) of the two after the collision? (Enter the magnitude.) X rad/s = After (0) (c) What is the total linear momentum (in kg · m/s) before and after the collision? (Enter the magnitude.) kg. m/s Pbefore kg. m/s PafterConservation of Angular Momentum An example of conservation of angular momentum is jumping on a Merry-Go-Round. Watch this video (it starts part way through but the only thing you miss is the people pushing the Merry-Go-Round) to see someone jumping on a Merry-Gr-Round in motion like this problem. You can model the Merry-Go-Round as a solid disk with a radius of 3.00 m and a mass of 75.5 kg. Initially the Merry-Go-Round has an angular velocity 7.90 radians / second. Then the person jumps on and change the Moment of Inertia of the system. The person lands on the outer edge of the Merry-Go-Round and has a mass of 60.0 kg. What is the final angular velocity of the system after the person jumps on? You can treat the person that jumps on a point mass (which means they are significantly smaller than the radius of the Merry-Go-Round) for this problem. Your answer should have the following: 2 Decimal Places Correct SI Units Appropriate Signs for Vector quantity answers Answers must be in the…