A bicycle wheel of radius 0.290 m rolls without sliding on a horizontal surface at a constant angular speed of 17.0 rad/s. A piece of gum of mass 5.40 g is stuck to the rim as shown in the diagram. (a) What is the magnitude of the angular momentum of the gum when it is at location A relative to the points indicated below? 0.00772 0.0309 What is the perpendicular distance from the point C to the velocity vector of the particle when it is at A? kg · m2/s the center of the wheel, O v kg - m2/s the point of contact, C (b) What is the magnitude of the angular momentum of the gum when it is at the location B relative to the points indicated below if e = 22.0°? 0.001544 Compare this situation to the mass at A. How is this similar? kg · m2/s O 206 the center of the wheel,
A bicycle wheel of radius 0.290 m rolls without sliding on a horizontal surface at a constant angular speed of 17.0 rad/s. A piece of gum of mass 5.40 g is stuck to the rim as shown in the diagram. (a) What is the magnitude of the angular momentum of the gum when it is at location A relative to the points indicated below? 0.00772 0.0309 What is the perpendicular distance from the point C to the velocity vector of the particle when it is at A? kg · m2/s the center of the wheel, O v kg - m2/s the point of contact, C (b) What is the magnitude of the angular momentum of the gum when it is at the location B relative to the points indicated below if e = 22.0°? 0.001544 Compare this situation to the mass at A. How is this similar? kg · m2/s O 206 the center of the wheel,
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)...
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![### Angular Momentum of a Rolling Bicycle Wheel
#### Problem Statement:
A bicycle wheel of radius 0.290 m rolls without sliding on a horizontal surface at a constant angular speed of 17.0 rad/s. A piece of gum of mass 5.40 g is stuck to the rim as shown in the diagram.
#### Diagram Description:
The diagram shows a bicycle wheel with points labeled A, B, and C. The gum is located at point A on the rim of the wheel. Point B is also on the rim but at an angle θ with the vertical passing through the wheel's center. Point C represents the point of contact between the wheel and the ground. The center of the wheel is labeled O.
##### Questions and Answers:
**(a) What is the magnitude of the angular momentum of the gum when it is at location A relative to the points indicated below?**
1. **Relative to the center of the wheel, O:**
- Answer: **0.00772 kg·m²/s** (This is correct as indicated by the check mark)
2. **Relative to the point of contact, C:**
- Answer: **0.0309 kg·m²/s** (This is incorrect as indicated by the cross mark)
- Comment: What is the perpendicular distance from the point C to the velocity vector of the particle when it is at A?
**(b) What is the magnitude of the angular momentum of the gum when it is at location B relative to the points indicated below if θ = 22.0°?**
1. **Relative to the center of the wheel, O:**
- Answer: **0.001544 kg·m²/s** (This is incorrect as indicated by the cross mark)
- Comment: Compare this situation to the mass at A. How is this similar?
2. **Relative to the point of contact, C:**
- Answer: **0.296 kg·m²/s** (This is incorrect as indicated by the cross mark)
- Comment: What is the perpendicular distance from the point C to the velocity vector of the particle when it is at B? Note that the magnitude of the linear speed remains the same.
#### Explanation:
The angular momentum of a particle relative to a point can be found using:
\[ L = r \times p \]
where \( r \) is the position vector of the particle relative to the point and \( p](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0afef86-41bd-49f7-9deb-bb70dd2f5172%2Ff074b82f-fab0-4a2c-b15e-1d85fda4de09%2F2sfu193.png&w=3840&q=75)
Transcribed Image Text:### Angular Momentum of a Rolling Bicycle Wheel
#### Problem Statement:
A bicycle wheel of radius 0.290 m rolls without sliding on a horizontal surface at a constant angular speed of 17.0 rad/s. A piece of gum of mass 5.40 g is stuck to the rim as shown in the diagram.
#### Diagram Description:
The diagram shows a bicycle wheel with points labeled A, B, and C. The gum is located at point A on the rim of the wheel. Point B is also on the rim but at an angle θ with the vertical passing through the wheel's center. Point C represents the point of contact between the wheel and the ground. The center of the wheel is labeled O.
##### Questions and Answers:
**(a) What is the magnitude of the angular momentum of the gum when it is at location A relative to the points indicated below?**
1. **Relative to the center of the wheel, O:**
- Answer: **0.00772 kg·m²/s** (This is correct as indicated by the check mark)
2. **Relative to the point of contact, C:**
- Answer: **0.0309 kg·m²/s** (This is incorrect as indicated by the cross mark)
- Comment: What is the perpendicular distance from the point C to the velocity vector of the particle when it is at A?
**(b) What is the magnitude of the angular momentum of the gum when it is at location B relative to the points indicated below if θ = 22.0°?**
1. **Relative to the center of the wheel, O:**
- Answer: **0.001544 kg·m²/s** (This is incorrect as indicated by the cross mark)
- Comment: Compare this situation to the mass at A. How is this similar?
2. **Relative to the point of contact, C:**
- Answer: **0.296 kg·m²/s** (This is incorrect as indicated by the cross mark)
- Comment: What is the perpendicular distance from the point C to the velocity vector of the particle when it is at B? Note that the magnitude of the linear speed remains the same.
#### Explanation:
The angular momentum of a particle relative to a point can be found using:
\[ L = r \times p \]
where \( r \) is the position vector of the particle relative to the point and \( p
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