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Problem 4: 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 = 1.1 meters, and a mass M= 286 kg. A small boy of mass m = 41 kg runs tangentially to the merry-go-round at a speed of v = 2.5 m/s, and jumps on. Randomized Variables R= 1.1 meters M= 286 kg m = 41 kg v = 2.5 m/s Part (a) Calculate the moment of inertia of the merry-go-round, in kg m m2. I= 1()7 89 E A 4 sin() cos() tan() HOME cotan() asin() acos() 5 6 atan() acotan() sinh() 2 3 cosh() tanh() cotanh() END - O Degrees Radians VO BACKSPACE DEL CLEAR Feedback I give up! Submit Hint Part (b) Immediately before the boy jumps on the merry go round, calculate his angular speed (in radians/second) about the central axi 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 a 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 t go-round when the boy is half way between the edge and the center of the merry go round? +

Problem 4: 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 = 1.1 meters, and a mass M= 286 kg. A small boy of mass m = 41 kg runs tangentially to the merry-go-round at a speed of v = 2.5 m/s, and jumps on. Randomized Variables R= 1.1 meters M= 286 kg m = 41 kg v = 2.5 m/s Part (a) Calculate the moment of inertia of the merry-go-round, in kg m m2. I= 1()7 89 E A 4 sin() cos() tan() HOME cotan() asin() acos() 5 6 atan() acotan() sinh() 2 3 cosh() tanh() cotanh() END - O Degrees Radians VO BACKSPACE DEL CLEAR Feedback I give up! Submit Hint Part (b) Immediately before the boy jumps on the merry go round, calculate his angular speed (in radians/second) about the central axi 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 a 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 t go-round when the boy is half way between the edge and the center of the merry go round? +

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Problem 4:** A merry-go-round is a playground ride that consists of a large disk mounted to rotate freely in a horizontal plane. The merry-go-round shown is initially at rest, has a radius \( R = 1.1 \) meters, and a mass \( M = 286 \) kg. A small boy with mass \( m = 41 \) kg runs tangentially to the merry-go-round at a speed \( v = 2.5 \) m/s, and jumps on. **Randomized Variables:** - \( R = 1.1 \) meters - \( M = 286 \) kg - \( m = 41 \) kg - \( v = 2.5 \) m/s **Part (a):** Calculate the moment of inertia of the merry-go-round, in kg·m². \[ I = \] Calculator interface with trigonometric and arithmetic functions is provided for computations, including options for using degrees or radians. **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 halfway between the edge and the center of the merry-go-round? **Part (e):** 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? **Part (f):** 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? **Illustration:** The image shows a colorful sketch of a merry-go-round with a child running towards it. The child is depicted next to the merry-go-round. Each part is accompanied by an icon indicating
Transcribed Image Text:**Problem 4:** A merry-go-round is a playground ride that consists of a large disk mounted to rotate freely in a horizontal plane. The merry-go-round shown is initially at rest, has a radius \( R = 1.1 \) meters, and a mass \( M = 286 \) kg. A small boy with mass \( m = 41 \) kg runs tangentially to the merry-go-round at a speed \( v = 2.5 \) m/s, and jumps on. **Randomized Variables:** - \( R = 1.1 \) meters - \( M = 286 \) kg - \( m = 41 \) kg - \( v = 2.5 \) m/s **Part (a):** Calculate the moment of inertia of the merry-go-round, in kg·m². \[ I = \] Calculator interface with trigonometric and arithmetic functions is provided for computations, including options for using degrees or radians. **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 halfway between the edge and the center of the merry-go-round? **Part (e):** 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? **Part (f):** 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? **Illustration:** The image shows a colorful sketch of a merry-go-round with a child running towards it. The child is depicted next to the merry-go-round. Each part is accompanied by an icon indicating
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