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The masses m1 = 1 kg, m2 = 2 kg and m3 = 3 kg are distributed as shown in the figure.
a) Find the coordinates of the center of mass.
b) Calculate the moments of inertia with respect to the x, y and z axes.
(z-axis is perpendicular to the screen plane and towards you).
![y (m)
2.
m1
m3:
1.
2.
3.
x (m)
-1
m,
2]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6cfeb50d-a183-4bc4-afb0-811a931a660d%2F3cd25f3d-6174-41ed-bb48-fbee4e19fb3c%2Fl3xvn6_processed.jpeg&w=3840&q=75)

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- Consider the system shown below where four point masses are connected to each other by massless rods. Two of the masses are m = 3 kg and the other two have the masses of M = 2 kg. If a = 1.4 m, b = 1.3 m and the system rotates about x-axis, determine the moment of inertia of the system. Express your answer in units of kg. m² using one decimal place. Answer: M a m m b b a M-xConsider a yoyo, where you have a string wrapped around a uniform solid cylinder of mass Y (70.0 g) and radius Ry. The moment of inertia of the yoyo is 5.60 x 105 kg m?. From rest, the yoyo starts to fall. a) Find the radius of the yoyo, given the moment of inertia for a cylinder disk is given by 1 = MR². b) Draw a free body diagram of the yoyo. c) Calculate the acceleration of the yoyo as it falls. Is the value you got for acceleration what you expected? Explain you answer. Calculate the tension force in the string? d)please solve symbolically before using numbers
- The three 160 g masses in (Figure 1) are connected by massless, rigid rods. a) What is the triangle’s moment of inertia about the axis through the center? b) What is the triangle’s kinetic energy if it rotates about the axis at 5.2 rev/srev/s ? Express your answer with the appropriate units.Consider the objects labeled A, B, C, and D shown in the figure. IA A *1 = B Each object is composed of identical thin sticks of uniformly distributed mass 2.39 kg and length 0.303 m. What are the moments of inertia IA, IB, IC, and Ip of the objects about a rotation axis perpendicular to the screen and passing through the black dot displayed on each object? Ic = kg.m² kg.m² IB = ID= D || kg.m² kg.m²A 0.8 m Mass Moment of Inertia. For each system, find the mass moment of inertia about an axis going through Point A (perpendicular to the paper). c. Point A is in the upper left corner of the object shown. It has a uniform area density of 120 kg/m². 0.4 m 0.8 m A - 0.4 m 120 kg/m² 0.4 m 0.4 m d. The system is 15kg uniform isosceles triangle with a height of 0.33m and a base of 0.26m. Point A is at the lower left corner of the triangle. m = 15 kg 0.26 m 0.33 m
- A uniform thin rod of mass m = 3.2 kg and length L = 1.5 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 6.5 N, F2 = 2.5 N, F3 = 15 N and F4 = 15 N. F2 acts a distance d = 0.14 m from the center of mass. a. Calculate the magnitude τ4 of the torque due to force F4 in newton meters. b. Calculate the angular acceleration α of the thin rod about its center of mass in radians per square second. Let the counter-clockwise direction be positive.Suppose we want to calculate the moment of inertia of a 65.5 kg skater, relative to a vertical axis through their center of mass. a. First calculate the moment of inertia (in kg⋅m2) when the skater has their arms pulled inward by assuming they are cylinder of radius 0.125 m. b. Now calculate the moment of inertia of the skater (in kg⋅m2) with their arms extended by assuming that each arm is 5% of the mass of their body. Assume the body is a cylinder of the same size, and the arms are 0.875 m long rods extending straight out from the center of their body being rotated at the ends.Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the longer sides and is parallel to the shorter sides? Group of answer choices 2.7 kg⋅m2 3.6 kg⋅m2 1.6 kg⋅m2 3.1 kg⋅m2 4.1 kg⋅m2
- A trapeze artist performs an aerial maneuver. While in a tucked position, as shown in Figure A, she rotates about her center of mass at a rate of ωi=5.79 rad/s. Her moment of inertia about this axis is ?i=16.7 kg·m^2. A short time later, the aerialist is in the straight position, as shown in Figure B. If the moment of inertia about her center of mass in this position is now ?f=30.7 kg·m^2, what is her rotational speed ?f?While sunbathing on the balcony of your 3rd floor apartment, you notice a gorilla drop a m = 38.2 kg crate from rest from the roof of the 5-story building across the street. Since you just completed a course on surveying, you know that the two identical buildings are d = 29 m apart, and have floors that are h = 5.1 m tall. The first floor is at ground level, as shown.a. Determine the magnitude of the angular momentum of the crate, in kilogram meters squared per second, as observed by you as it passes the floor of the 4th floor balcony of the other building. Lb =b. Determine the magnitude of the angular momentum of the crate, in kilogram meters squared per second, as observed by you as it passes the floor of the 3rd floor balcony of the other building, directly across from you. Lc =c. Determine the magnitude of the angular momentum of the crate, in kilogram meters squared per second, as observed by you as it passes the floor of the 2nd floor balcony of the other building. Ld =d.…Help please