Three light rods of negligible mass are joined to form an equilateral triangle of length L = 1.90 m. Three masses m1 = 5.00 kg, m2 = 7.00 kg, and m3 = 9.00 kg are fixed to the vertices of this triangle as shown in the diagram below. Treat the masses as point particles.
(a) What is the moment of inertia of the system about an axis lying in the plane of the triangle, passing through the midpoint of one side and the opposite vertex as shown by the dashed line?
(b) What is the moment of inertia of the system about an axis passing through the center of the triangle and perpendicular to its plane?
Three light rods of negligible mass are joined to form an equilateral triangle of length L = 1.90 m.
Three objects, each of mass m are arranged in an equilateral triangle, with side length L. The mass of the connecting rods is negligible. a.) If the system is rotating around a vertical axis passing through the upper vertex of the triangle, what is the system's moment of inertia in terms of its total mass? b.) If the system is rotating around a horizontal axis passing through the upper vertex of the triangle, what is the system's moment of inertia...
Three identical point masses of mass M are fixed at the comers of an equilateral triangle of sides I as shown. Axis Aruns through a point equidistant from all three masses, perpendicular to the plane of the triangle. Axis B runs through M, and is perpendicular to the plane of the triangle. Axes C, D, and E, lie in the plane of the triangle and are as shown. Part (a) Determine an expression in terms of M and / for the...
011. Four particles with masses 4 kg, 6 kg, 4 kg, and 6 kg are connected by rigid rods of negligible mass as shown. The origin is centered on the mass in the lower left corner. The rectangle is 6 m wide and 5 m long. If the system rotates in the xy plane about the z axis (origin, O) with an angular speed of 5 rad/s, calculate the moment of inertia of the system about the z axis. 012. Find the...
QUESTION 1 A dumbell consists of two identical masses of mass M attached to a either end of a rod of length 2X and of negligible mass. If the dumbell is rotated about an axis perpendicular to the rod and passing through the middle of the rod, as shown in the diagram. What is the rotational inertia of the dumbell? Axis. -*-X ←-ㄧㄧㄨ 2Mx2 2M2x MX2 M2x QUESTION 2 Two identical uniform thin rods of length 0.542 m and mass...
1. (25 pts.) Three particles are at the vertices of a rigid, massless equilateral triangle, whose sides are L = 4.0 m. Their masses are mi = 10 kg, m2 = 20 kg and m3 = 30 kg. a. Find the x and y coordinates of the center of mass of the system, with respect to the point P halfway along the base. b. Find the moment of inertia if the system is free to rotate around an axis down...
The three masses in the figure lie in a horizontal plane. They are fixed at the corners of an isosceles triangle with light rigid rods. Assume the masses are point sized objects. a. Find the center of mass position relative to the origin. b. Find the moment of inertia of the masses about an axis parallel to the z-axis and located at the midpoint of BC. c. Find the moment of inertia of the masses about an axis parallel to...
A 1.0 kg mass is located at the origin of the (?, ?) plane, another 1.0 kg mass is located at the point (0.12, 0), and a 2.0 kg mass is located at the point (0.06, 0.08), where the (?, ?) coordinates are given in meters. The three masses are fixed relative to each other by massless rods. a) Find the moment of inertia of this object about an object perpendicular to the (?, ?) plane & passing through the...
Three objects with mass m, 2m and 3m are connected by light rods of length d and located in the xy-plane as shown in the figure. a) Calculate the coordinates of the center of mass. b) Calculate the moment of inertia for rotation about the z-axis. y - m d х 3m 2m
Three objects with mass m, 2m and 3m are connected by light rods of length d and located in the xy-plane as shown in the figure. a) Calculate the coordinates of the center of mass. b) Calculate the moment of inertia for rotation about the z-axis. y - m d х 3m 2m
Four identical particles of mass m each are placed at the vertices of a square with side length a and held by four massless rods, which form the sides of the square. (Use any variable stated above.) a. What is the rotational inertia of this rigid body about an axis passes through the midpoint of opposite sides and lies in the plane of the square? b. What is the rotational inertia of this rigid body about an axis that passes through...