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4. Consider the sketch of the setup for this experiment above. Assume that the tension in the string running over the pulley is T = 10 N and the radius of the pulley is R = 10 cm. The torque acting on the pulley is %3D (a) 100 N m (b) 10 N m (c) 1Nm (d) 0.1 N m (e) 0.01 N m

4. Consider the sketch of the setup for this experiment above. Assume that the tension in the string running over the pulley is T = 10 N and the radius of the pulley is R = 10 cm. The torque acting on the pulley is %3D (a) 100 N m (b) 10 N m (c) 1Nm (d) 0.1 N m (e) 0.01 N m

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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Please answer question number 4 with all steps thank you!
**Educational Text on Moment of Inertia of Earth** 1. **Problem Statement:** Determine the moment of inertia \( I \) of the Earth on its path around the Sun. Use the following values: - **Mass of the Earth:** \( M_E = 6 \times 10^{24} \) kg - **Radius of the Earth's orbit around the Sun:** \( R_{ES} = 150 \times 10^6 \) km **Options for \( I \):** - (a) \( I = 1.35 \times 10^{41} \, \text{kg} \cdot \text{m}^2 \) - (b) \( I = 5.4 \times 10^{46} \, \text{kg} \cdot \text{m}^2 \) - (c) \( I = 6.75 \times 10^{46} \, \text{kg} \cdot \text{m}^2 \) - (d) \( I = 1.35 \times 10^{47} \, \text{kg} \cdot \text{m}^2 \) 2. **Question on Change in Earth's Year Length:** Consider problem 1. How would the value you found for \( I \) change if the Earth's year were only half as long (i.e., 182.5 days instead of 365 days)? **Options:** - (a) The value of \( I \) would double. - (b) The value of \( I \) would be half. - (c) The value of \( I \) would not change. - (d) The value of \( I \) would quadruple. - (e) The value of \( I \) would be one quarter. 3. **Question on Change in Orbit Radius:** Consider problem 1. How would the value you found for \( I \) change if the radius of the Earth's path around the Sun were only half as large (i.e., 75 × 10^6 km instead of 150 × 10^6 km)? (Note: The text above discusses determining the moment of inertia of Earth in its orbit and explores hypothetical scenarios affecting \( I \). There are no graphs or diagrams in this text.)
Transcribed Image Text:**Educational Text on Moment of Inertia of Earth** 1. **Problem Statement:** Determine the moment of inertia \( I \) of the Earth on its path around the Sun. Use the following values: - **Mass of the Earth:** \( M_E = 6 \times 10^{24} \) kg - **Radius of the Earth's orbit around the Sun:** \( R_{ES} = 150 \times 10^6 \) km **Options for \( I \):** - (a) \( I = 1.35 \times 10^{41} \, \text{kg} \cdot \text{m}^2 \) - (b) \( I = 5.4 \times 10^{46} \, \text{kg} \cdot \text{m}^2 \) - (c) \( I = 6.75 \times 10^{46} \, \text{kg} \cdot \text{m}^2 \) - (d) \( I = 1.35 \times 10^{47} \, \text{kg} \cdot \text{m}^2 \) 2. **Question on Change in Earth's Year Length:** Consider problem 1. How would the value you found for \( I \) change if the Earth's year were only half as long (i.e., 182.5 days instead of 365 days)? **Options:** - (a) The value of \( I \) would double. - (b) The value of \( I \) would be half. - (c) The value of \( I \) would not change. - (d) The value of \( I \) would quadruple. - (e) The value of \( I \) would be one quarter. 3. **Question on Change in Orbit Radius:** Consider problem 1. How would the value you found for \( I \) change if the radius of the Earth's path around the Sun were only half as large (i.e., 75 × 10^6 km instead of 150 × 10^6 km)? (Note: The text above discusses determining the moment of inertia of Earth in its orbit and explores hypothetical scenarios affecting \( I \). There are no graphs or diagrams in this text.)
**Educational Content on Rotational Motion** --- **Section M-8: Rotational Motion** 1. **Hypothetical Changes in Moment of Inertia (I)** (a) The value of \( I \) would double. (b) The value of \( I \) would be half. (c) The value of \( I \) would not change. (d) The value of \( I \) would quadruple. (e) The value of \( I \) would be one quarter. 2. **Torque Calculation** Consider the sketch of the setup for this experiment above. Assume that the tension in the string running over the pulley is \( T = 10 \, \text{N} \) and the radius of the pulley is \( R = 10 \, \text{cm} \). The torque acting on the pulley is: (a) \( 100 \, \text{Nm} \) (b) \( 10 \, \text{Nm} \) (c) \( 1 \, \text{Nm} \) (d) \( 0.1 \, \text{Nm} \) (e) \( 0.01 \, \text{Nm} \) 3. **Angular Acceleration** Consider problem 4 above. Assuming the pulley is a cylindrical, solid disk of mass \( M = 5 \, \text{kg} \), the angular acceleration of the pulley is closest to: (a) \( 0.2 \, \text{rads}^{-2} \) (b) \( 2 \, \text{rads}^{-2} \) (c) \( 4 \, \text{rads}^{-2} \) (d) \( 20 \, \text{rads}^{-2} \) (e) \( 40 \, \text{rads}^{-2} \) 4. **Moment of Inertia—Figure Skater Example** During a pirouette, a figure skater reduces her moment of inertia from \( I_1 = 1.24 \, \text{kg m}^2 \) to \( I_2 = 0.25 \, \text{kg m}^
Transcribed Image Text:**Educational Content on Rotational Motion** --- **Section M-8: Rotational Motion** 1. **Hypothetical Changes in Moment of Inertia (I)** (a) The value of \( I \) would double. (b) The value of \( I \) would be half. (c) The value of \( I \) would not change. (d) The value of \( I \) would quadruple. (e) The value of \( I \) would be one quarter. 2. **Torque Calculation** Consider the sketch of the setup for this experiment above. Assume that the tension in the string running over the pulley is \( T = 10 \, \text{N} \) and the radius of the pulley is \( R = 10 \, \text{cm} \). The torque acting on the pulley is: (a) \( 100 \, \text{Nm} \) (b) \( 10 \, \text{Nm} \) (c) \( 1 \, \text{Nm} \) (d) \( 0.1 \, \text{Nm} \) (e) \( 0.01 \, \text{Nm} \) 3. **Angular Acceleration** Consider problem 4 above. Assuming the pulley is a cylindrical, solid disk of mass \( M = 5 \, \text{kg} \), the angular acceleration of the pulley is closest to: (a) \( 0.2 \, \text{rads}^{-2} \) (b) \( 2 \, \text{rads}^{-2} \) (c) \( 4 \, \text{rads}^{-2} \) (d) \( 20 \, \text{rads}^{-2} \) (e) \( 40 \, \text{rads}^{-2} \) 4. **Moment of Inertia—Figure Skater Example** During a pirouette, a figure skater reduces her moment of inertia from \( I_1 = 1.24 \, \text{kg m}^2 \) to \( I_2 = 0.25 \, \text{kg m}^
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