Problem 3: An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: 0(t) = a + bt2 - ct³ where a = 1.1 rad, b = 0.45 rad/s2 and c 0.035 rad/s3. Randomized Variables a = 1.1 rad b = 0.45 rad/s2 c = 0.035 rad/s3 Part (a) Determine an equation for the angular speed of the ride as a function of time, w(t). Expression : w(t) = Select from the variables below to write your expression. Note that all variables may not be required. B, 0, a, b, c, d, g, h, j, k, m, n, P, S, t Part (b) Besides at t 0, at what time tį is the ride stopped? Give your answer in seconds. Numeric : A numeric value is expected and not an expression. t = Part (c) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t? Numeric : A numeric value is expected and not an expression. A0 =

Problem 3: An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: 0(t) = a + bt2 - ct³ where a = 1.1 rad, b = 0.45 rad/s2 and c 0.035 rad/s3. Randomized Variables a = 1.1 rad b = 0.45 rad/s2 c = 0.035 rad/s3 Part (a) Determine an equation for the angular speed of the ride as a function of time, w(t). Expression : w(t) = Select from the variables below to write your expression. Note that all variables may not be required. B, 0, a, b, c, d, g, h, j, k, m, n, P, S, t Part (b) Besides at t 0, at what time tį is the ride stopped? Give your answer in seconds. Numeric : A numeric value is expected and not an expression. t = Part (c) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t? Numeric : A numeric value is expected and not an expression. A0 =

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter8: Central-force Motion

Section: Chapter Questions

Problem 8.45P

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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…
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