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 = 1.2 meters, and a mass M = 211 kg. A small boy of mass m = 41 kg runs tangentially to the merry-go-round at a speed of v = 1.4 m/s, and jumps on. R = 1.2 meters M = 211 kg m = 41 kg v = 1.4 m/s Calculate the moment of inertia of the merry-go-round, in kg ⋅ m2. I = 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. ω1 = Immediately after the boy jumps on the merry go round, calculate the angular speed in radians/second of the merry-go-round and boy. ω2 = 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? ω3 = 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? ω4 = 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 ground with zero velocity with respect to the ground. What is the angular speed in radians/second of the merry-go-round after the boy jumps off? ω5 =
Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
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 = 1.2 meters, and a mass M = 211 kg. A small boy of mass m = 41 kg runs tangentially to the merry-go-round at a speed of v = 1.4 m/s, and jumps on.
R = 1.2 meters
M = 211 kg
m = 41 kg
v = 1.4 m/s
Calculate the moment of inertia of the merry-go-round, in kg ⋅ m2.
I =
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.
| ω1 = |
Immediately after the boy jumps on the merry go round, calculate the angular speed in radians/second of the merry-go-round and boy.
ω2 =
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?
ω3 =
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?
ω4 =
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 ground with zero velocity with respect to the ground. What is the angular speed in radians/second of the merry-go-round after the boy jumps off?
ω5 =
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