Problem 4: A uniform wooden meter stick has a mass of m = 601 g. A clamp can be attached to the measuring stick at any point P along the stick so that the stuck can rotate freely about point P, which is at a distance d from the zero-end of the stick as shown. Randomized Variables 304 5 6 8. 10 11 12 13 14 15 16 17 18 m = 601 g d
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8.4 please answer parts d-f, other parts are answered
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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 = 1.3 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…Suppose you start an antique car by exerting a force of 250 N on its crank for 0.34 s.Randomized Variablesf = 250 Nt = 0.34 sd = 0.36 m What angular momentum is given to the engine if the handle of the crank is 0.36 m from the pivot and the force is exerted to create maximum torque the entire time?
- 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 = 291 kg. A small boy of mass m = 42 kg runs tangentially to the merry-go-round at a speed of v = 1.8 m/s, and jumps on. Randomized VariablesR = 1.3 metersM = 291 kgm = 42 kgv = 1.8 m/s Part 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. Part 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. Part 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…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/sA 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…
- Consider a compact disc as a thick walled cylinder of mass 16.0 g, and with an outer diameter of 11.6 cm and inner diameter of 4.6 cm. Find the (a) moment of inertia of the compact disc about an axis passing through its center and (b) moment of inertia of the compact disc about an axis passing through its edge parallel to the previous axis.Prove that the moment of inertia of a solid sphere of uniform density, when rotating around a diameter,is 2MR2/5, where M is the mass of the sphere and R is the radius.Hint: integrate the infinitesimal volume element in spherical coordinates.The four masses shown in the diagram are connected by massless, rigid rods. The mass of the A particle is 400 g, the mass of the B particle is 650 g, the mass of the C particle is 700 g, and the mass of the D particle is 550 g. The length of the rods is 40 cm. Consider the A particle to be the origin of the coordinate system. Find the moment of inertia (in kg*m*m) about an axis that passes through mass A and is perpendicular to the page. The x coordinate of the center of mass (in cm) is 21.7 cm. Consider the A particle to be the origin of the coordinate system. They coordinate of the center of mass (in cm) is 23.5 cm
- A uniform rod of mass 200 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 20 g, are mounted in grooves along the rod. Initially, the two beads are held by catches on opposite sides of the rod’s center, 10 cm from the axis of rotation. With the beads in this position, the rod is rotating with an angular velocity of 10.0 rad/s. When the catches are released, the beads slide outward along the rod. (a) What is the rod’s angular velocity when the beads reach the ends of the rod? (b) What is the rod’s angular velocity if the beads fly off the rod?Find the moment (Nm) caused by the force F = 803 N about point A if a = 27 mm and b = 31 mm.A rod of mass M = 3.25 kg and length L can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m = 65 g, moving with speed v = 5.25 m/s, strikes the rod at angle θ = 51° from the normal at a distance D = 2/3 L, where L = 1.3 m, from the point of rotation and sticks to the rod after the collision. 1. What is the angular speed ωf of the system immediately after the collision, in radians per second?