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*43. Go The drawing shows two identical systems of objects; each consists of the same three small balls connected by massless rods. In both systems the axis is perpendicular to the page, but it is located at a different place, as shown. The same force of magnitude F is applied to the same ball in each system (see the drawing). The masses of the balls are m₁ = 9.00 kg, 6.00 kg, and m3 7.00 kg. The magnitude of the force is F = 424 N. (a) For each of the two systems, determine the moment of inertia about the given axis of rotation. (b) Calculate the torque (magnitude and direc- tion) acting on each system. (c) Both systems start from rest, and the direction of the force moves with the system and always points along the 4.00-m rod. What is the angular velocity of each system after 5.00 s? m₂ - m1 Axis = 3.00 m 5.00 m System A F m2 4.00 m m3 m1 3.00 m 5.00 m Axis. System B F m2 4.00 m m3

*43. Go The drawing shows two identical systems of objects; each consists of the same three small balls connected by massless rods. In both systems the axis is perpendicular to the page, but it is located at a different place, as shown. The same force of magnitude F is applied to the same ball in each system (see the drawing). The masses of the balls are m₁ = 9.00 kg, 6.00 kg, and m3 7.00 kg. The magnitude of the force is F = 424 N. (a) For each of the two systems, determine the moment of inertia about the given axis of rotation. (b) Calculate the torque (magnitude and direc- tion) acting on each system. (c) Both systems start from rest, and the direction of the force moves with the system and always points along the 4.00-m rod. What is the angular velocity of each system after 5.00 s? m₂ - m1 Axis = 3.00 m 5.00 m System A F m2 4.00 m m3 m1 3.00 m 5.00 m Axis. System B F m2 4.00 m m3

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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Physics Ch. 9 #43

## Understanding Rotational Dynamics with Two Identical Systems ### Problem Statement The drawing illustrates two identical systems, each composed of three small balls connected by massless rods. In both systems, the axis is perpendicular to the page, positioned at different locations. A force of magnitude \( F \) is applied to the same ball in each system. - Masses of the balls: - \( m_1 = 9.00 \, \text{kg} \) - \( m_2 = 6.00 \, \text{kg} \) - \( m_3 = 7.00 \, \text{kg} \) - Magnitude of the force: \( F = 424 \, \text{N} \) ### Questions (a) Determine the moment of inertia for each system about the given axis of rotation. (b) Calculate the torque (magnitude and direction) acting on each system. (c) Both systems start from rest, and the direction of the force rotates with the system, always pointing along the 4.00-m rod. What is the angular velocity of each system after 5.00 s? ### Diagram Explanation - **System A:** - The axis is positioned closer to \( m_1 \). - \( m_1 \) (green) is 3.00 m away from the axis. - \( m_2 \) (orange) is 4.00 m away from the axis. - \( m_3 \) (red) is 5.00 m away from the axis. - Force \( F \) is applied downwards at \( m_2 \). - **System B:** - The axis is positioned closer to \( m_3 \). - \( m_1 \) is 3.00 m away from \( m_2 \). - \( m_2 \) is 4.00 m away from the axis. - \( m_3 \) is 5.00 m away from \( m_2 \). - Force \( F \) is applied downwards at \( m_2 \). Both diagrams clearly indicate the distances between the masses and the axes of rotation, which are critical for calculating moments of inertia and torques.
Transcribed Image Text:## Understanding Rotational Dynamics with Two Identical Systems ### Problem Statement The drawing illustrates two identical systems, each composed of three small balls connected by massless rods. In both systems, the axis is perpendicular to the page, positioned at different locations. A force of magnitude \( F \) is applied to the same ball in each system. - Masses of the balls: - \( m_1 = 9.00 \, \text{kg} \) - \( m_2 = 6.00 \, \text{kg} \) - \( m_3 = 7.00 \, \text{kg} \) - Magnitude of the force: \( F = 424 \, \text{N} \) ### Questions (a) Determine the moment of inertia for each system about the given axis of rotation. (b) Calculate the torque (magnitude and direction) acting on each system. (c) Both systems start from rest, and the direction of the force rotates with the system, always pointing along the 4.00-m rod. What is the angular velocity of each system after 5.00 s? ### Diagram Explanation - **System A:** - The axis is positioned closer to \( m_1 \). - \( m_1 \) (green) is 3.00 m away from the axis. - \( m_2 \) (orange) is 4.00 m away from the axis. - \( m_3 \) (red) is 5.00 m away from the axis. - Force \( F \) is applied downwards at \( m_2 \). - **System B:** - The axis is positioned closer to \( m_3 \). - \( m_1 \) is 3.00 m away from \( m_2 \). - \( m_2 \) is 4.00 m away from the axis. - \( m_3 \) is 5.00 m away from \( m_2 \). - Force \( F \) is applied downwards at \( m_2 \). Both diagrams clearly indicate the distances between the masses and the axes of rotation, which are critical for calculating moments of inertia and torques.
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