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(i) Draw an extended free body diagram of a unicycle being pedaled on a gravel path (I have included a starting point for what the unicycle looks like). Assume there is friction from the gravel on the tire and the pedal is fixed at 90 degrees with respect to the lever arm. Also assume as you pedal, the pedal will not hit the ground (Rpedal < Rire, the diagram is not drawn to scale). O™ (ii) Write down Newton's second law for this situation. Label and define any radii, forces, moment of inertia, masses etc so I know what each variable means. Please break each variable down to base components/definitions (i.e. FG = mg). (iii) If we are "spinning out" aka the tire spins and the unicycle does not move forward, does your extended free body diagram change? If so, how? What condition can we no longer use?

(i) Draw an extended free body diagram of a unicycle being pedaled on a gravel path (I have included a starting point for what the unicycle looks like). Assume there is friction from the gravel on the tire and the pedal is fixed at 90 degrees with respect to the lever arm. Also assume as you pedal, the pedal will not hit the ground (Rpedal < Rire, the diagram is not drawn to scale). O™ (ii) Write down Newton's second law for this situation. Label and define any radii, forces, moment of inertia, masses etc so I know what each variable means. Please break each variable down to base components/definitions (i.e. FG = mg). (iii) If we are "spinning out" aka the tire spins and the unicycle does not move forward, does your extended free body diagram change? If so, how? What condition can we no longer use?

College Physics
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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### Understanding the Physics of a Pedaled Unicycle on a Gravel Path **Objective:** By the end of this exercise, you will be able to: 1. Draw and label an extended free body diagram (FBD) of a unicycle. 2. Apply Newton’s second law to this scenario. 3. Identify changes in the FBD under specific conditions. --- **Part (i): Drawing the Extended Free Body Diagram of a Unicycle** Consider a unicycle being pedaled on a gravel path. To help you visualize the setup, the following conditions are given: - There is friction from the gravel on the tire. - The pedal is fixed at a 90-degree angle with respect to the lever arm. - As you pedal, the pedal will not hit the ground. This means \(R_{\text{pedal}} < R_{\text{tire}}\) (where the diagram is not drawn to scale). The attached diagram shows the extended free body diagram of the unicycle, which includes: - A large outer circle representing the tire. - A smaller inner circle representing the hub or central part of the wheel. - A horizontal line extending from the center of the inner circle representing the lever arm attached to the pedal. - An arrow pointing downward from the pedal symbolizing the force exerted on the pedal. --- **Part (ii): Writing Down Newton’s Second Law** For this scenario, apply Newton’s second law of motion. Label and define any radii, forces, moments of inertia, masses, etc. Here is how to break down each variable: - **Radii (R):** - \(R_{\text{tire}}\): Radius of the tire. - \(R_{\text{pedal}}\): Radius to the pedal point. - **Forces (F):** - \( \vec{F}_{\text{G}} = mg \) : Gravitational force acting on the unicycle. - **Moment of Inertia (I):** - Moment of inertia about the wheel. - **Acceleration (a):** - Linear acceleration of the unicycle. - Angular acceleration of the wheel. **Newton’s Second Law:** \( \sum \vec{F} = ma \) **Using Torque:** \( \sum \tau = I\alpha \) --- **Part (iii): Changing Conditions - Spinning Out** If the wheel spins out and the unicycle does not move forward, then the
Transcribed Image Text:### Understanding the Physics of a Pedaled Unicycle on a Gravel Path **Objective:** By the end of this exercise, you will be able to: 1. Draw and label an extended free body diagram (FBD) of a unicycle. 2. Apply Newton’s second law to this scenario. 3. Identify changes in the FBD under specific conditions. --- **Part (i): Drawing the Extended Free Body Diagram of a Unicycle** Consider a unicycle being pedaled on a gravel path. To help you visualize the setup, the following conditions are given: - There is friction from the gravel on the tire. - The pedal is fixed at a 90-degree angle with respect to the lever arm. - As you pedal, the pedal will not hit the ground. This means \(R_{\text{pedal}} < R_{\text{tire}}\) (where the diagram is not drawn to scale). The attached diagram shows the extended free body diagram of the unicycle, which includes: - A large outer circle representing the tire. - A smaller inner circle representing the hub or central part of the wheel. - A horizontal line extending from the center of the inner circle representing the lever arm attached to the pedal. - An arrow pointing downward from the pedal symbolizing the force exerted on the pedal. --- **Part (ii): Writing Down Newton’s Second Law** For this scenario, apply Newton’s second law of motion. Label and define any radii, forces, moments of inertia, masses, etc. Here is how to break down each variable: - **Radii (R):** - \(R_{\text{tire}}\): Radius of the tire. - \(R_{\text{pedal}}\): Radius to the pedal point. - **Forces (F):** - \( \vec{F}_{\text{G}} = mg \) : Gravitational force acting on the unicycle. - **Moment of Inertia (I):** - Moment of inertia about the wheel. - **Acceleration (a):** - Linear acceleration of the unicycle. - Angular acceleration of the wheel. **Newton’s Second Law:** \( \sum \vec{F} = ma \) **Using Torque:** \( \sum \tau = I\alpha \) --- **Part (iii): Changing Conditions - Spinning Out** If the wheel spins out and the unicycle does not move forward, then the
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