### Physics Problem: Angular Acceleration of Charged Balls in an Electric Field#### Problem Statement:Two 1.0 gram (g) balls are connected by a 2.0 centimeter (cm) long insulating rod of negligible mass. One ball has a charge of +10 nanocoulombs (nC), and the other has a charge of -10 nanocoulombs (nC). The rod is held in a uniform electric field of \(1.0 \times 10^4 \text{ N/C}\) at an angle of \(30^\circ\) with respect to the field and then released. Determine the rod's initial angular acceleration. The moment of inertia (I) of the system is given as \(2.0 \times 10^{-7} \text{ kg m}^2\).#### Explanation:1. **Mass and Charges**: - **Mass of each ball**: 1.0 gram (g), which is equivalent to \(1.0 \times 10^{-3}\) kilograms (kg). - **Charge of one ball**: +10 nanocoulombs (nC) which is \(+10 \times 10^{-9}\) coulombs (C). - **Charge of the other ball**: -10 nanocoulombs (nC) which is \(-10 \times 10^{-9}\) coulombs (C).2. **Rod Length**: - **Distance between the two balls**: 2.0 centimeters (cm), which is 0.02 meters (m).3. **Electric Field**: - **Magnitude**: \(1.0 \times 10^4 \text{ N/C}\) - **Angle with respect to the field**: \(30^\circ\)4. **Moment of Inertia (I)**: - \(2.0 \times 10^{-7} \text{ kg m}^2\)#### Objective: - Calculate the initial angular acceleration of the system once it is released.#### Solution Strategy:1. **Torque Calculation**: - The force on each charge due to the electric field can be calculated using \( \mathbf{F} = q \mathbf{E} \). - For the +10 nC charge: \( F_{+} = ( +10 \times 10^{-9} \text{

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Two 1.0 (g) balls are connected by a 2.0 (cm) long insulating rod of negligible mass. One ball has a charge of +10 (nC), the other a charge of -10 (nC). The rod is held in a 1.0 × 104 (N/C) uniform electric field at an angle of 30° with respect to the field, then released. What is its initial angular acceleration? Consider I = 2.0 × 10-7 (kg m?).

Two 1.0 (g) balls are connected by a 2.0 (cm) long insulating rod of negligible mass. One ball has a charge of +10 (nC), the other a charge of -10 (nC). The rod is held in a 1.0 × 104 (N/C) uniform electric field at an angle of 30° with respect to the field, then released. What is its initial angular acceleration? Consider I = 2.0 × 10-7 (kg m?).

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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