11 # Physics Problem 12.81: Angular Velocity of a Merry-Go-Round## Problem Description:A merry-go-round is a common piece of playground equipment. A 3.0-meter-diameter merry-go-round, which can be modeled as a disk with a mass of 250 kg, is spinning at 25 revolutions per minute (rpm). John runs tangent to the merry-go-round at 4.6 meters per second (m/s), in the same direction that it is turning, and jumps onto the outer edge. John's mass is 30 kg.### Part A:**Question:** What is the merry-go-round's angular velocity, in rpm, after John jumps on? Express your answer in revolutions per minute to two significant figures.**Answer Attempt:** Typed in: 23 rpm**Feedback:** ❌ Incorrect; Try Again, 5 attempts remaining### Explanation:You need to calculate the new angular velocity of the system after John jumps onto the merry-go-round. This involves applying the principle of conservation of angular momentum. The initial angular momentum of the system (merry-go-round + John) will equal the angular momentum after John jumps on.#### Given Data:- Diameter of the merry-go-round: 3.0 m- Mass of the merry-go-round: 250 kg- Initial angular velocity of the merry-go-round: 25 rpm- Velocity of John: 4.6 m/s- Mass of John: 30 kg#### Required:Calculate the new angular velocity in rpm.**Considerations for Calculation:**1. Determine the initial angular momentum of the merry-go-round.2. Calculate the angular momentum contributed by John as he jumps onto the merry-go-round.3. Apply the conservation of angular momentum to find the new angular velocity.Use these considerations to arrive at a correct answer and try submitting again.

Answered: Image /qna-images/answer/11e8fa76-d8ad-45ab-bbe5-c4aae6aa4851.jpg

A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round, which can be modeled as a disk with a mass of 250 kg, is spinning at 25 rpm. John runs tangent to the merry-go-round at 4.6 m/s, in the same direction that it is turning, and jumps onto the outer edge. John's mass is 30 kg. Part A What is the merry-go-round's angular velocity, in rpm, after John jumps on? Express your answer in revolutions per minute to two significant figures. VE ΑΣΦ 1 W= 23 Submit In ? rpm

A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round, which can be modeled as a disk with a mass of 250 kg, is spinning at 25 rpm. John runs tangent to the merry-go-round at 4.6 m/s, in the same direction that it is turning, and jumps onto the outer edge. John's mass is 30 kg. Part A What is the merry-go-round's angular velocity, in rpm, after John jumps on? Express your answer in revolutions per minute to two significant figures. VE ΑΣΦ 1 W= 23 Submit In ? rpm

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: 5. Vector directions in one dimension are represented by a. Distances b. Magnitude c. Signs d.…

A: Vector direction in one dimension is represented by a. Distance Not correct Distance is a scalar…

Q: Refer to diagram 3. A closed circular loop (N = 409 turns, radius r= 6.6 cm, resistance R = 3.65 Q)…

A: Formula of induced current is as follows; I=εR…

Q: Q: If A- fi+2f) and E - fi+2f]+ 3f k,fis constant, find the angle between these two vectors?

Q: Which one to use

A: If you're asking where to post computer science questions, there are several options depending on…

Q: [P,P2] = -iħ o -1 O ih o o

A: Ques:

Q: Given vectors p and a have a magnitude of 7 and 2, respectively. Find the magnitude and direction of…

A: Magnitude of p = 7 Magnitude of q = 2 Angle, θ = 150°

Q: 46. A ship travels 50.0 mi on a course of 15.0° south of east and then travels 85.5 mi on a course…

Q: 8. Find R = Ã+B, given that A has a magnitude of 4 at an angle of 30° above positive x-axis and B…

Q: A car starts from the origin and is driven 1.25 km south, then 8.75 km in a direction 57° north of…

A: Given value--- firstly driven 1.25 km south, then 8.75 km in a direction 57° north of east. We…

Q: A hill that has a 32.5% grade is one that rises 32.5 m vertically for every 100.0 m of distance in…

Q: Which of the following plots produce a line with slope equal to 6.626 x 10 34 J s? Select all that…

Q: add the vectors

A: For the first figure, the vector equation is

Q: Vecrors of length 10 and 15 have a Cross product of 150 if i add those vectors, what is the length…

A: The dot product of the two vectors is,

Q: Part A - Finding the length of the hypotenuse of the first triangle For the first triangle, what is…

Q: add the vector

A: Let the three vectors be denoted as A, B and C.Resolve the three vectors along the coordinate axes…

Q: Select the correct statement for: “If the vector has a magnitude of 25 meters and make an angle of…

A: The magnitude of a vector is the length of the vector and the angle is the orientation from the axis…

Q: 5. Vector A S has a magnitude of 35.0 units and points in the direction 325° counterclockwise from…

A: Given : |A| = 35 units θ = 325° counterclockwise from the positive x axis

Q: Ã = (5 m/s)î + (2 m/s)j, B = (3 kg · m/s²)î + (2 kg · m/s²)I %3D

Q: A vector has an x-component of 2.64 and a y-component of 4.58. The magnitude of the vector is:

A: The objective of the question is to find the magnitude of a vector given its x and y components. The…

Q: Part C Enter the expression -20 + 6D in the answer box using the notation just described. Express…

Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

# Physics Problem 12.81: Angular Velocity of a Merry-Go-Round

## Problem Description:

A merry-go-round is a common piece of playground equipment. A 3.0-meter-diameter merry-go-round, which can be modeled as a disk with a mass of 250 kg, is spinning at 25 revolutions per minute (rpm). John runs tangent to the merry-go-round at 4.6 meters per second (m/s), in the same direction that it is turning, and jumps onto the outer edge. John's mass is 30 kg.

### Part A:

**Question:**
What is the merry-go-round's angular velocity, in rpm, after John jumps on? Express your answer in revolutions per minute to two significant figures.

**Answer Attempt:**
Typed in: 23 rpm

**Feedback:**
❌ Incorrect; Try Again, 5 attempts remaining

### Explanation:

You need to calculate the new angular velocity of the system after John jumps onto the merry-go-round. This involves applying the principle of conservation of angular momentum. The initial angular momentum of the system (merry-go-round + John) will equal the angular momentum after John jumps on.

#### Given Data:

- Diameter of the merry-go-round: 3.0 m
- Mass of the merry-go-round: 250 kg
- Initial angular velocity of the merry-go-round: 25 rpm
- Velocity of John: 4.6 m/s
- Mass of John: 30 kg

#### Required:

Calculate the new angular velocity in rpm.

**Considerations for Calculation:**

1. Determine the initial angular momentum of the merry-go-round.
2. Calculate the angular momentum contributed by John as he jumps onto the merry-go-round.
3. Apply the conservation of angular momentum to find the new angular velocity.

Use these considerations to arrive at a correct answer and try submitting again.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Calculation of the angular velocity of the after the jump.

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Convert the following Vectors given in polar coordinates (r, q) to the equivalent Vector in cartesian coordinates (x, y). Check significant figures. C = (12.0, 34) b. F = (5.00, 45.0o )
A 3.09-kg particle is subject to a net force that varies with position as shown in the figure. The particle starts from rest at x = 0. F, (N) 3 1 x (m) 2 4 6 8 10 12 14 16' What is its speed at the following positions?
A = 3î + î + 23 43, B = ?
1. Calculate the resultant vector based on the information given in figure 1. 50.0 N 60.0⁰ K 30.0⁰ 49.0 N
The resultant vector R has an angle that is determined by
Two vectors a and 6 have magnitudes 4 and 2 respectively. Also the angle between a and bis Find a .. 130
. Calculate the area of the parallelogram whose two adjacent sides are formed by the vectors. A = 31 + 4k B = 23+k.
10. What is the acceleration (m/s2) for an incline with an angle 23.3 degrees?
1. Express the force as representation. a Cartesian vector or Rectangular F= 50 lb 45°
An airplane left an airport and flew 105 mi in the direction of North 50.4000 deg E, then turned and flew 493 mi in the direction of South 11.9000 deg E. How far (mi) and in what direction should it return to the the airport?
axis
Vector A has a magnitude of 17.0 units, vector B has a magnitude of 15.0 units, and A B has a value of 14.0. What is the angle between the directions of A and B? Number Units