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1. Two point masses a mass a-6 Kg mass and...
A 1.0 kg mass is located at the origin of the (?, ?) plane, another 1.0...
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...
2. Two point masses m and m2 are separated by a massless rod of length L....
2. Two point masses m and m2 are separated by a massless rod of length L. (a) Write an expression for the moment of inertia I about an axis perpendicular to the rod and passing through it a distance x from mass mi. (b) Calculate dl/dx and show that I is at a minimum when the axis passes through the center of mass of the system.
QUESTION 1 A dumbell consists of two identical masses of mass M attached to a either...
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...
Four particles with masses 4 kg, 6 kg, 4 kg, and 6 kg are connected by rigid rods of negligible mass as shown.
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...
6. (BONUS) Two particles each with mass m = 0.4 kg, are fastened to each other,...
6. (BONUS) Two particles each with mass m = 0.4 kg, are fastened to each other, and to a rotation axis at 0, by the two thin rods, each of length d and mass M = 1.5 kg as shown below. The combination rotates around the rotation axis with angular speed w = 0.2 rad/s. The total moment of inertia of the system measured about O is 2.3 x 10-4 kg m?. (Hint: The moment of inertia of a thin...
A very thin, straight, uniform rod has a length of 3.00 m and a total mass...
A very thin, straight, uniform rod has a length of 3.00 m and a total mass of 7.00 kg. Treating the rod as essentially a line segment of mass (distributed uniformly), do the following: (i) Use integration to prove that the rod's center of mass is located at its center point. (Reminders: dmnds mass (and that axis is perpendicular to the rod). with the previous result-to calculate lemr the moment of inertia of the rod about an axis through one...
Three small spherical masses are located in a plane at the positions shown below. 4 R...
Three small spherical masses are located in a plane at the positions shown below. 4 R 2 1 -1 -2 -3 -4 1 2 3 4 -5 -4 -3 -2 -1 X (m) The masses are Q 0.200 kg, R=0.300 kg, and S 0.400 kg. Calculate the moment of inertia (of the 3 masses) with respect to an àxis perpendicular to the xy plane and passing through x-0 and y-2. [Since the masses are of small size, you can neglect...
Ball a, of mass , is connected to ball b, of mass , by a massless rod of length . The two vertical dashed lines in...
Ball a, of mass ma, is
connected to ball b, of mass mb, by a
massless rod of length L. The two
vertical dashed lines in the figure, one througheach ball,
represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular
to the rod. The moment of inertia of the two-masssystem about axis a is Ia, and the
moment of inertia of the system about axis b is Ib. It is
observed that the ratio...
Four point masses, each of mass 1.1 kg are placed at the corners of a square...
Four point masses, each of mass 1.1 kg are placed at the corners of a square of side 1.6 m. A. Find the moment of inertia of this system about an axis that is perpendicular to the plane of the square and passes through one of the masses. B. If the system is set rotating about the above axis with kinetic energy of 195.0 J, what is the number of revolutions the system makes per minute
Two masses my and my are attached to a rod that is capable of rotating about...
Two masses my and my are attached to a rod that is capable of rotating about an axis perpendicular to the rod and passing through the end A as shown in the diagram below. The length of the rod is L = 17.0 cm, mı = 2.00 g, m2 = 3.50 9, X1 = 5.40 cm and x2 = 8.55 cm. L m m A X2 *1 (a) What is the moment of inertia of the system about the specified...
2. Two point masses m and m2 are separated by a massless rod of length L. (a) Write an expression for the moment of inertia I about an axis perpendicular to the rod and passing through it a distance x from mass mi. (b) Calculate dl/dx and show that I is at a minimum when the axis passes through the center of mass of the system.
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...
6. (BONUS) Two particles each with mass m = 0.4 kg, are fastened to each other, and to a rotation axis at 0, by the two thin rods, each of length d and mass M = 1.5 kg as shown below. The combination rotates around the rotation axis with angular speed w = 0.2 rad/s. The total moment of inertia of the system measured about O is 2.3 x 10-4 kg m?. (Hint: The moment of inertia of a thin...
A very thin, straight, uniform rod has a length of 3.00 m and a total mass of 7.00 kg. Treating the rod as essentially a line segment of mass (distributed uniformly), do the following: (i) Use integration to prove that the rod's center of mass is located at its center point. (Reminders: dmnds mass (and that axis is perpendicular to the rod). with the previous result-to calculate lemr the moment of inertia of the rod about an axis through one...
Three small spherical masses are located in a plane at the positions shown below. 4 R 2 1 -1 -2 -3 -4 1 2 3 4 -5 -4 -3 -2 -1 X (m) The masses are Q 0.200 kg, R=0.300 kg, and S 0.400 kg. Calculate the moment of inertia (of the 3 masses) with respect to an àxis perpendicular to the xy plane and passing through x-0 and y-2. [Since the masses are of small size, you can neglect...
Ball a, of mass ma, is
connected to ball b, of mass mb, by a
massless rod of length L. The two
vertical dashed lines in the figure, one througheach ball,
represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular
to the rod. The moment of inertia of the two-masssystem about axis a is Ia, and the
moment of inertia of the system about axis b is Ib. It is
observed that the ratio...
Two masses my and my are attached to a rod that is capable of rotating about an axis perpendicular to the rod and passing through the end A as shown in the diagram below. The length of the rod is L = 17.0 cm, mı = 2.00 g, m2 = 3.50 9, X1 = 5.40 cm and x2 = 8.55 cm. L m m A X2 *1 (a) What is the moment of inertia of the system about the specified...
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