### Physics Problem on Rotational Motion: Motorcycle Wheel Dynamics**Problem Overview:**Consider an **11.0 kg motorcycle wheel** shown in the figure.![Motorcycle Wheel Diagram](#)Assume it to be approximately an annular ring with an inner radius of \( R_1 = 0.280 \, \text{m} \) and an outer radius of \( R_2 = 0.440 \, \text{m} \). The motorcycle is on its center stand, so that the wheel can spin freely.### Given Data:- **Mass of the wheel**: \( 11.0 \, \text{kg} \)- **Inner radius**: \( R_1 = 0.280 \, \text{m} \)- **Outer radius**: \( R_2 = 0.440 \, \text{m} \)- **Force exerted by the drive chain**: \( 2320 \, \text{N} \)- **Radius where the force is applied**: \( 5.00 \, \text{cm} \) (or \( 0.050 \, \text{m} \))### Questions:**(a)** If the drive chain exerts a force of \( 2320 \, \text{N} \) at a radius of \( 5.00 \, \text{cm} \), what is the angular acceleration (in \( \text{rad/s}^2 \)) of the wheel?\[ \boxed{\text{rad/s}^2} \]**(b)** What is the tangential acceleration (in \( \text{m/s}^2 \)) of a point on the outer edge of the tire?\[ \boxed{\text{m/s}^2} \]**(c)** How long (in \( \text{s} \)), starting from rest, does it take to reach an angular velocity of \( 80.0 \, \text{rad/s} \)?\[ \boxed{\text{s}} \]---### Explanation of Diagrams:**Diagram Analysis:**- The diagram shows a cross-sectional view of the motorcycle wheel annotated with key parameters including radii \( R_1 \) and \( R_2 \), and the point where the force \( F \) is applied.- \( \alpha \) denotes the angular parameters

Answered: Image /qna-images/answer/0a51c4f3-1bd4-4b7f-af18-b1910c4574ac.jpg

ssume it to be approximately an annular ring with an inner radius of R, = 0.280 m and an outer radius of R, = 0.440 m. The motorcycle is on its center stand, so that the wheel can spin freely. a) If the drive chain exerts a force of 2320 N at a radius of 5.00 cm, what is the angular acceleration (in rad/s?) of the wheel? rad/s² b) What is the tangential acceleration (in m/s?) of a point on the outer edge of the tire? ]m/s² c) How long (in s), starting from rest, does it take to reach an angular velocity of 80.0 rad/s?

ssume it to be approximately an annular ring with an inner radius of R, = 0.280 m and an outer radius of R, = 0.440 m. The motorcycle is on its center stand, so that the wheel can spin freely. a) If the drive chain exerts a force of 2320 N at a radius of 5.00 cm, what is the angular acceleration (in rad/s?) of the wheel? rad/s² b) What is the tangential acceleration (in m/s?) of a point on the outer edge of the tire? ]m/s² c) How long (in s), starting from rest, does it take to reach an angular velocity of 80.0 rad/s?

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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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

### Physics Problem on Rotational Motion: Motorcycle Wheel Dynamics

**Problem Overview:**
Consider an **11.0 kg motorcycle wheel** shown in the figure.

![Motorcycle Wheel Diagram](#)

Assume it to be approximately an annular ring with an inner radius of \( R_1 = 0.280 \, \text{m} \) and an outer radius of \( R_2 = 0.440 \, \text{m} \). The motorcycle is on its center stand, so that the wheel can spin freely.

### Given Data:
- **Mass of the wheel**: \( 11.0 \, \text{kg} \)
- **Inner radius**: \( R_1 = 0.280 \, \text{m} \)
- **Outer radius**: \( R_2 = 0.440 \, \text{m} \)
- **Force exerted by the drive chain**: \( 2320 \, \text{N} \)
- **Radius where the force is applied**: \( 5.00 \, \text{cm} \) (or \( 0.050 \, \text{m} \))

### Questions:
**(a)** If the drive chain exerts a force of \( 2320 \, \text{N} \) at a radius of \( 5.00 \, \text{cm} \), what is the angular acceleration (in \( \text{rad/s}^2 \)) of the wheel?

\[ \boxed{\text{rad/s}^2} \]

**(b)** What is the tangential acceleration (in \( \text{m/s}^2 \)) of a point on the outer edge of the tire?

\[ \boxed{\text{m/s}^2} \]

**(c)** How long (in \( \text{s} \)), starting from rest, does it take to reach an angular velocity of \( 80.0 \, \text{rad/s} \)?

\[ \boxed{\text{s}} \]

---

### Explanation of Diagrams:
**Diagram Analysis:**
- The diagram shows a cross-sectional view of the motorcycle wheel annotated with key parameters including radii \( R_1 \) and \( R_2 \), and the point where the force \( F \) is applied.
- \( \alpha \) denotes the angular parameters

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