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A yoyo is made of two wooden disks connected by a central axel as shown below. A string is wound around the axel so that when the yoyo is released, it unwinds while moving downward. Suppose the yoyo is released from rest and allowed to fall 5.00 meters. What will be its linear velocity at its lowest point? Mass of each disk, ma = 100 grams (1 kg – 1000 grams) Radius of each disk Rd= 3.00 cm (1 m = Radius of axel Ra = 5.00 mm (1 m= 1000 mm) Mass of axel is negligible. - 100 cm)

A yoyo is made of two wooden disks connected by a central axel as shown below. A string is wound around the axel so that when the yoyo is released, it unwinds while moving downward. Suppose the yoyo is released from rest and allowed to fall 5.00 meters. What will be its linear velocity at its lowest point? Mass of each disk, ma = 100 grams (1 kg – 1000 grams) Radius of each disk Rd= 3.00 cm (1 m = Radius of axel Ra = 5.00 mm (1 m= 1000 mm) Mass of axel is negligible. - 100 cm)

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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### Exploring the Physics of a Yoyo A yoyo consists of two wooden disks connected by a central axle. A string is wound around the axle so that when the yoyo is released, it unwinds while moving downward. **Problem Statement:** Imagine the yoyo is released from rest and allowed to fall 5.00 meters. What will its linear velocity be at its lowest point? **Specifications:** - **Mass of each disk (md):** 100 grams (1 kg = 1000 grams) - **Radius of each disk (Rd):** 3.00 cm (1 m = 100 cm) - **Radius of axle (Ra):** 5.00 mm (1 m = 1000 mm) - **Mass of axle:** Negligible **Diagrams:** - The diagram on the left shows a side view of the yoyo, illustrating how the string is wrapped around the axle between the two disks. - The diagram on the right provides a perspective view, showing the dimensions and arrangement of the disks and the axle. This scenario allows us to analyze rotational and translational motion, exploring concepts such as energy conservation, rotational inertia, and dynamics.
Transcribed Image Text:### Exploring the Physics of a Yoyo A yoyo consists of two wooden disks connected by a central axle. A string is wound around the axle so that when the yoyo is released, it unwinds while moving downward. **Problem Statement:** Imagine the yoyo is released from rest and allowed to fall 5.00 meters. What will its linear velocity be at its lowest point? **Specifications:** - **Mass of each disk (md):** 100 grams (1 kg = 1000 grams) - **Radius of each disk (Rd):** 3.00 cm (1 m = 100 cm) - **Radius of axle (Ra):** 5.00 mm (1 m = 1000 mm) - **Mass of axle:** Negligible **Diagrams:** - The diagram on the left shows a side view of the yoyo, illustrating how the string is wrapped around the axle between the two disks. - The diagram on the right provides a perspective view, showing the dimensions and arrangement of the disks and the axle. This scenario allows us to analyze rotational and translational motion, exploring concepts such as energy conservation, rotational inertia, and dynamics.
**FORMULAS** 1. **Kinematic Rotational Equations:** - \( s = r\theta \) - \( v = r\omega \) - \( a = r\alpha \) 2. **Torque:** - \( \tau = F(\sin\theta)r \) - \( \tau = Fl \), where \( l \) is the lever arm 3. **Equilibrium and Non-equilibrium:** - Equilibrium: \( \Sigma \tau = 0 \) - Non-equilibrium: \( \Sigma \tau = I\alpha \) 4. **Moments of Inertia for Various Rigid Objects of Uniform Composition:** - Point mass: \( I = MR^2 \) **Diagram Explanation: Moments of Inertia for Various Rigid Objects of Uniform Composition** 1. **Hoop or Thin Cylindrical Shell:** - Image shows a hoop with rotation around its central axis. - Moment of Inertia: \( I = MR^2 \) 2. **Solid Sphere:** - Image shows a solid sphere. - Moment of Inertia: \( I = \frac{2}{5} MR^2 \) 3. **Solid Cylinder or Disk:** - Image shows a solid cylinder. - Moment of Inertia: \( I = \frac{1}{2} MR^2 \) 4. **Thin Spherical Shell:** - Image shows a thin shell of a sphere. - Moment of Inertia: \( I = \frac{2}{3} MR^2 \) 5. **Long, Thin Rod with Rotation Axis Through Center:** - Image shows a long rod rotating about its center. - Moment of Inertia: \( I = \frac{1}{12} ML^2 \) 6. **Long, Thin Rod with Rotation Axis Through End:** - Image shows a long rod with rotation about one end. - Moment of Inertia: \( I = \frac{1}{3} ML^2 \) These formulas and diagrams are essential for understanding the rotational dynamics of various rigid objects.
Transcribed Image Text:**FORMULAS** 1. **Kinematic Rotational Equations:** - \( s = r\theta \) - \( v = r\omega \) - \( a = r\alpha \) 2. **Torque:** - \( \tau = F(\sin\theta)r \) - \( \tau = Fl \), where \( l \) is the lever arm 3. **Equilibrium and Non-equilibrium:** - Equilibrium: \( \Sigma \tau = 0 \) - Non-equilibrium: \( \Sigma \tau = I\alpha \) 4. **Moments of Inertia for Various Rigid Objects of Uniform Composition:** - Point mass: \( I = MR^2 \) **Diagram Explanation: Moments of Inertia for Various Rigid Objects of Uniform Composition** 1. **Hoop or Thin Cylindrical Shell:** - Image shows a hoop with rotation around its central axis. - Moment of Inertia: \( I = MR^2 \) 2. **Solid Sphere:** - Image shows a solid sphere. - Moment of Inertia: \( I = \frac{2}{5} MR^2 \) 3. **Solid Cylinder or Disk:** - Image shows a solid cylinder. - Moment of Inertia: \( I = \frac{1}{2} MR^2 \) 4. **Thin Spherical Shell:** - Image shows a thin shell of a sphere. - Moment of Inertia: \( I = \frac{2}{3} MR^2 \) 5. **Long, Thin Rod with Rotation Axis Through Center:** - Image shows a long rod rotating about its center. - Moment of Inertia: \( I = \frac{1}{12} ML^2 \) 6. **Long, Thin Rod with Rotation Axis Through End:** - Image shows a long rod with rotation about one end. - Moment of Inertia: \( I = \frac{1}{3} ML^2 \) These formulas and diagrams are essential for understanding the rotational dynamics of various rigid objects.
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