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An oversized yo-yo is made from two identical solid disks each of mass M = 2.10 kg and radius R = 10.0 cm. The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 ko as in the figure below. Take the center of the cylinder as the axis of the system.

An oversized yo-yo is made from two identical solid disks each of mass M = 2.10 kg and radius R = 10.0 cm. The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 ko as in the figure below. Take the center of the cylinder as the axis of the system.

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### An Oversized Yo-Yo System An oversized yo-yo is made from two identical solid disks, each with a mass \(M = 2.10 \, \text{kg}\) and a radius \(R = 10.0 \, \text{cm}\). The two disks are joined by a solid cylinder with a radius \(r = 4.00 \, \text{cm}\) and a mass \(m = 1.00 \, \text{kg}\), as illustrated in the figure below. The center of the cylinder is considered the axis of the system. ![Yo-Yo Diagram](yo-yo_diagram.png) *(Diagram shows a cylindrical yo-yo with two large disks connected by a smaller central cylinder)* #### Problem Set (a) **What is the moment of inertia of the system?** Provide a symbolic answer using any given variables or symbols. **Moment of inertia \([ \underline{\phantom{Moment of inertia}} ]\):** (b) **What torque does gravity exert on the system with respect to the given axis?** **Torque (N·m):** \([ \underline{\phantom{Torque}} ]\) *Take downward as the negative coordinate direction.* (c) **As depicted in the figure above, is the torque exerted by the tension positive or negative?** *(Consider the yo-yo from the left and let the counterclockwise direction be positive.)* - [ ] positive - [ ] negative (d) **Is the angular acceleration positive or negative?** - [ ] positive - [ ] negative (e) **What about the translational acceleration?** - [ ] positive - [ ] negative (f) **Write an equation for the angular acceleration \(\alpha\) in terms of the translational acceleration \(a\) and radius \(r\).** (*Watch the sign!*) \(\alpha = [ \underline{\phantom{\alpha}} ]\) --- ### Diagram Explanation The diagram demonstrates a yo-yo system comprised of two identical large disks connected by a smaller central cylinder. The large disks and the central cylinder represent different mass and radius values, crucial for calculating the moment of inertia and other dynamic properties. The system's axis runs through the center of the central cylinder, and it serves as the reference point for measuring torque, angular velocity, and acceleration.
Transcribed Image Text:### An Oversized Yo-Yo System An oversized yo-yo is made from two identical solid disks, each with a mass \(M = 2.10 \, \text{kg}\) and a radius \(R = 10.0 \, \text{cm}\). The two disks are joined by a solid cylinder with a radius \(r = 4.00 \, \text{cm}\) and a mass \(m = 1.00 \, \text{kg}\), as illustrated in the figure below. The center of the cylinder is considered the axis of the system. ![Yo-Yo Diagram](yo-yo_diagram.png) *(Diagram shows a cylindrical yo-yo with two large disks connected by a smaller central cylinder)* #### Problem Set (a) **What is the moment of inertia of the system?** Provide a symbolic answer using any given variables or symbols. **Moment of inertia \([ \underline{\phantom{Moment of inertia}} ]\):** (b) **What torque does gravity exert on the system with respect to the given axis?** **Torque (N·m):** \([ \underline{\phantom{Torque}} ]\) *Take downward as the negative coordinate direction.* (c) **As depicted in the figure above, is the torque exerted by the tension positive or negative?** *(Consider the yo-yo from the left and let the counterclockwise direction be positive.)* - [ ] positive - [ ] negative (d) **Is the angular acceleration positive or negative?** - [ ] positive - [ ] negative (e) **What about the translational acceleration?** - [ ] positive - [ ] negative (f) **Write an equation for the angular acceleration \(\alpha\) in terms of the translational acceleration \(a\) and radius \(r\).** (*Watch the sign!*) \(\alpha = [ \underline{\phantom{\alpha}} ]\) --- ### Diagram Explanation The diagram demonstrates a yo-yo system comprised of two identical large disks connected by a smaller central cylinder. The large disks and the central cylinder represent different mass and radius values, crucial for calculating the moment of inertia and other dynamic properties. The system's axis runs through the center of the central cylinder, and it serves as the reference point for measuring torque, angular velocity, and acceleration.
### Physics Problem Set #### Questions: (g) **Write Newton's second law for the system in terms of \( m, M, a, T, \) and \( g \).** (Do this on paper. Your instructor may ask you to turn in this work.) (h) **Write Newton's second law for rotation in terms of \( I, \alpha, T, \) and \( r \).** (Do this on paper. Your instructor may ask you to turn in this work.) (i) **Eliminate \( \alpha \) from the rotational second law with the expression found in part (f) and find a symbolic expression for the acceleration \( a \) in terms of \( m, M, g, r, \) and \( R \).** \[ a = \, \_\_\_ \] (j) **What is the numeric value for the system's acceleration?** \[ \_\_\_ \text{ m/s}^2 \] (k) **What is the tension in the string?** \[ \_\_\_ \text{ N} \] (l) **How long does it take the system to drop 0.80 m from rest?** \[ \_\_\_ \text{ s} \]
Transcribed Image Text:### Physics Problem Set #### Questions: (g) **Write Newton's second law for the system in terms of \( m, M, a, T, \) and \( g \).** (Do this on paper. Your instructor may ask you to turn in this work.) (h) **Write Newton's second law for rotation in terms of \( I, \alpha, T, \) and \( r \).** (Do this on paper. Your instructor may ask you to turn in this work.) (i) **Eliminate \( \alpha \) from the rotational second law with the expression found in part (f) and find a symbolic expression for the acceleration \( a \) in terms of \( m, M, g, r, \) and \( R \).** \[ a = \, \_\_\_ \] (j) **What is the numeric value for the system's acceleration?** \[ \_\_\_ \text{ m/s}^2 \] (k) **What is the tension in the string?** \[ \_\_\_ \text{ N} \] (l) **How long does it take the system to drop 0.80 m from rest?** \[ \_\_\_ \text{ s} \]
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