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PROBLEM 1 (10 POINTS) A particle of mass m is located at x = 2, y = 0, z = 3. (a) Find its moment...
I want the answer just for (((Q 3)))) Thanks!!!! 2. A triangular prism of mass M,...
I want the answer just for (((Q 3))))
Thanks!!!!
2. A triangular prism of mass M, whose two ends are equilateral triangles parallel to the xy plane with side 2a, is centered on the origin with its axis along the z-axis. Find its moment of inertia for rotation about its z-axis. Without doing any integrals write down and explain its two products of inertia for rotation about the z-axis Hint: You can find the rotational inertia of an equilateral triangle...
Three small objects are located in the x-y plane as shown in the figure. The objects...
Three small objects are located in the x-y plane as shown in the figure. The objects have the following masses: mA 1.93 kg, mB- 2.09 kg, mc 3.67 kg. x (m) What is the moment of inertia of this set of objects with respect to the axis perpendicular to the the x-y plane passing through location x =5.00 m and у = 4.00 m? The objects are small in size, their moments of inertia about their own centers of mass...
Earth with mass M. The angular velocity magnitude of the Earth relative to the inertial frame,...
Earth with mass M. The angular velocity magnitude of the Earth relative to the inertial frame, Ω. Find any cross products in this problem. This problem will have calculation in the non inertial frame S which rotates with the Earth about its axis. Earth is motionless in the S frame. The xyz coordinate system originates at the center of the Earth, the North Pole is on the positive z axis. At t = 0, a ball of mass m is...
Find the Moment of inertia of: a) The rectangular solid formed by 0≤x≤a,0≤y≤b, and 0≤z≤c by...
Find the Moment of inertia of:
a) The rectangular solid formed by 0≤x≤a,0≤y≤b, and 0≤z≤c by
calculating Ix, Iy, Iz. [Hint:
Compute one of the moments directly and then reason about the other
cases via symmetry].
b) The x, y and z axes of a thin plate bounded by the parabola
x=−y2 and the line x=−y with the density function
defined as δ(x,y) = 1/y.
Find the Moment of inertia of: (a) (15 points) The rectangular solid formed by 0...
#1 A particle of mass, m, moves along the path with its coordinates given as functions...
#1 A particle of mass, m, moves along the path with its coordinates given as functions of time: x=x, +at?, y = bt, z=ct, where xq, a,b,c are constants. Find angular momentum of this particle with respect to the origin, force acting on this particle and torque acting on this particle with respect to the origin as functions of time. Verify that your results satisfy Newton's second de law for rotation, which is " =FxF.
Problem 3. (24 points) A uniform rod of mass M and length d is free to...
Problem 3. (24 points) A uniform rod of mass M and length d is free to pivot about one end. The moment of inertia of the rod about the pivot is I = Md2/3, and the rod's center of mass is at its midpoint. The rod is released from rest at angle above the horizontal, then rotates downward under the influence of gravity. d x e When the rod reaches angle below the horizontal, determine (a) (4 points) the rotational...
(a) A uniform disk of mass 14 kg, thickness 0.5 m, and radius 0.4 m is located at the origin, oriented with its axis al...
(a) A uniform disk of mass 14 kg, thickness 0.5 m, and radius 0.4 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the +y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.5 s. What is the rotational angular momentum of the disk? What is the rotational kinetic...
A small particle of mass m is at rest on a horizontal circular platform that is...
A small particle of mass m is at rest on a horizontal circular platform that is free to rotate about a vertical axis through its center. The particle is located at a radius r from the axis, as shown in the figure above. The platform begins to rotate with constant angular acceleration α . Because of friction between the particle and the platform, the particle remains at rest with respect to the platform. When the platform has reached angular speed...
Three small spherical masses are located in plane at the positions shown below. 4 3 1...
Three small spherical masses are located in plane at the positions shown below. 4 3 1 G 3 1 2 3 4 5 -5 -4 -3 -2 -1 0 X (m) The masses are Q 0.700 kg, R-0.400 kg, and S-0.800 kg. Calculate the moment of inertia (of the 3 masses) with respect to an axis perpendicular to the xy plane and passing through x-0 and y-2. [Since the masses are of small size, you can neglect the contribútion due...
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on...
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on an inclined plane with inclination angle ? in the gravitational field g. Follow the steps below to find the velocity V of the center of mass of the sphere as a function of time if the sphere is initially at rest. Bold font represents vectors. There exists a reaction force R at the point of contact between the sphere and the plane. The equations...
I want the answer just for (((Q 3))))
Thanks!!!!
2. A triangular prism of mass M, whose two ends are equilateral triangles parallel to the xy plane with side 2a, is centered on the origin with its axis along the z-axis. Find its moment of inertia for rotation about its z-axis. Without doing any integrals write down and explain its two products of inertia for rotation about the z-axis Hint: You can find the rotational inertia of an equilateral triangle...
Three small objects are located in the x-y plane as shown in the figure. The objects have the following masses: mA 1.93 kg, mB- 2.09 kg, mc 3.67 kg. x (m) What is the moment of inertia of this set of objects with respect to the axis perpendicular to the the x-y plane passing through location x =5.00 m and у = 4.00 m? The objects are small in size, their moments of inertia about their own centers of mass...
Find the Moment of inertia of:
a) The rectangular solid formed by 0≤x≤a,0≤y≤b, and 0≤z≤c by
calculating Ix, Iy, Iz. [Hint:
Compute one of the moments directly and then reason about the other
cases via symmetry].
b) The x, y and z axes of a thin plate bounded by the parabola
x=−y2 and the line x=−y with the density function
defined as δ(x,y) = 1/y.
Find the Moment of inertia of: (a) (15 points) The rectangular solid formed by 0...
#1 A particle of mass, m, moves along the path with its coordinates given as functions of time: x=x, +at?, y = bt, z=ct, where xq, a,b,c are constants. Find angular momentum of this particle with respect to the origin, force acting on this particle and torque acting on this particle with respect to the origin as functions of time. Verify that your results satisfy Newton's second de law for rotation, which is " =FxF.
Problem 3. (24 points) A uniform rod of mass M and length d is free to pivot about one end. The moment of inertia of the rod about the pivot is I = Md2/3, and the rod's center of mass is at its midpoint. The rod is released from rest at angle above the horizontal, then rotates downward under the influence of gravity. d x e When the rod reaches angle below the horizontal, determine (a) (4 points) the rotational...
(a) A uniform disk of mass 14 kg, thickness 0.5 m, and radius 0.4 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the +y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.5 s. What is the rotational angular momentum of the disk? What is the rotational kinetic...
A small particle of mass m is at rest on a horizontal circular platform that is free to rotate about a vertical axis through its center. The particle is located at a radius r from the axis, as shown in the figure above. The platform begins to rotate with constant angular acceleration α . Because of friction between the particle and the platform, the particle remains at rest with respect to the platform. When the platform has reached angular speed...
Three small spherical masses are located in plane at the positions shown below. 4 3 1 G 3 1 2 3 4 5 -5 -4 -3 -2 -1 0 X (m) The masses are Q 0.700 kg, R-0.400 kg, and S-0.800 kg. Calculate the moment of inertia (of the 3 masses) with respect to an axis perpendicular to the xy plane and passing through x-0 and y-2. [Since the masses are of small size, you can neglect the contribútion due...
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on an inclined plane with inclination angle ? in the gravitational field g. Follow the steps below to find the velocity V of the center of mass of the sphere as a function of time if the sphere is initially at rest. Bold font represents vectors. There exists a reaction force R at the point of contact between the sphere and the plane. The equations...
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