### Rotational Inertia CalculationIn this exercise, we will calculate the rotational inertia of three masses with respect to the y-axis. The position and mass of each body are given below:- **Mass 1 (m1)**: - Mass: 3.5 units - Position: \( x_1 = 4.4 \), \( y_1 = -2.6 \)- **Mass 2 (m2)**: - Mass: 5.0 units - Position: \( x_2 = -4.4 \), \( y_2 = -2.8 \)- **Mass 3 (m3)**: - Mass: 3.0 units - Position: \( x_3 = -3.2 \), \( y_3 = -2.6 \)### ExplanationRotational inertia (also known as moment of inertia) with respect to the y-axis, \( I_y \), can be calculated using the formula:\[ I_y = \sum m_i \cdot x_i^2 \]where:- \( m_i \) is the mass of the ith object.- \( x_i \) is the x-coordinate of the ith object.Using the provided data, we can calculate the total rotational inertia around the y-axis by summing the contributions of each individual mass.### Detailed StepsFor each mass, we will compute the product of the mass and the square of its x-coordinate.1. **Mass 1 (m1 = 3.5)**: \[ I_{y1} = m1 \cdot x1^2 = 3.5 \cdot (4.4)^2 \]2. **Mass 2 (m2 = 5.0)**: \[ I_{y2} = m2 \cdot x2^2 = 5.0 \cdot (-4.4)^2 \]3. **Mass 3 (m3 = 3.0)**: \[ I_{y3} = m3 \cdot x3^2 = 3.0 \cdot (-3.2)^2 \]Summing these values will give the total rotational inertia with respect to the y-axis:\[ I_y = I_{y1} + I_{y2} + I_{y3} \]

Answered: Find the rotational inertia of the…

Science

Physics

Find the rotational inertia of the following masses with respect to the y-axis:

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)...

See similar textbooks

Similar questions

Please help me with this
What is the angular momentum of a 0.315 kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 12.0 rad/s ? Express your answer using three significant figures and include the appropriate units.
An automobile traveling 76.0 km/h has tires of 80.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 19.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding) (a) Number i (b) Number i (c) Number i Units Units Units
A 550-g uniform sphere of 7.3-cm radius spins frictionless at 32 rev per sec on an axis through its center. Find its (a) KE (b) angular momentum, and (c) radius of gyration.
An automobile traveling 70.0 km/h has tires of 64.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 25.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding) (a) Number i Units (b) Number i Units (c) Number i Units
Two point masses are the same distance R from an axis of rotation and have moments of inertia IA and IB. (a) If IB = 16IA, what is the ratio mB mA of the two masses? (b) In terms of R, at what distance from the axis of rotation should mass A be placed so that IA = IB?
Solve the problem and provide the solution
An automobile traveling 55.0 km/h has tires of 71.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 21.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding) (a) Number i Units (b) Number i Units (c) Number i Units
Two particles of identical mass mare acted on only by the gravitational force of one upon the other. If the distance d between the particles is constant, what is the angular velocity of the line joining them? Use Newton's second law with the center of mass of the system as the origin of the inertial frame.
a 0.400 kg ball is shot directly upward at initial speed 76.5 m/s. What is its angular momentum about P, 8.72 m horizontally from the launch point, when the ball is (a) at maximum height and (b) halfway back to the ground? What is the torque on the ball about P due to the gravitational force when the ball is (c) at maximum height and (d) halfway back to the ground? i need the answered to d
An automobile traveling 62.0 km/h has tires of 61.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 15.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding) (a) Number i Units (b) Number i Units (c) Number Units
An automobile traveling 89.0 km/h has tires of 76.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 18.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding) (a) Number i Units (b) Number i Units (c) Number i Units