### 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

Given information: Here, r is the wheel’s radius, ω is the angular speed of the wheel, m is the…

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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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.

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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

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