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Find the rotational kinetic energy for the next system if it rotates at a rate of...
A cylinder with rotational inertia I1 = 3.2 kg · m2 rotates clockwise about a vertical...
A cylinder with rotational inertia I1 = 3.2 kg · m2 rotates clockwise about a vertical axis through its center with angular speed ω1 = 5.8 rad/s. A second cylinder with rotational inertia I2 = 1.2 kg · m2 rotates counterclockwise about the same axis with angular speed ω2 = 6.2 rad/s. If the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s)? What percentage of the original kinetic energy...
rods of negligible mass lying along the y axis connect three particles. The system rotates about...
rods of negligible mass lying along the y axis connect three particles. The system rotates about the x axis with an angular peed of 3.70 rad/s. (a) Find the moment of inertia about the x axis. kg middot m^2 (b) Find the total rotational kinetic energy evaluated from 1/2 I omega^2. J (c) Find the tangential speed of each particle. 4.00 kg particle m/s 2.00 kg particle m/s 3.00 kg particle m/s (d) Find the total kinetic energy evaluated from...
Match the units with the rotational quantity: Moment of inertia Angular acceleration Torque Rotational kinetic energy...
Match the units with the rotational quantity: Moment of inertia Angular acceleration Torque Rotational kinetic energy Angular Momentum a. kg·m2/s b. J c. N·m d. kg m2 e. rad s-2
Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total pot...
Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of, and (2) Derive the equations of motion using Lagrangian equation method, (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode shapes if m-30 g, 4-8 x...
6. (20) Energy conservation analysis: Use conse frictional force, to directy find the kinetic ene...
6. (20) Energy conservation analysis: Use conse frictional force, to directy find the kinetic energy of the sysin ysis: Use the conservation of energy, coupled with the work done by the when m2 hits the ground. With that ds a symbolic relation involving u, m, m2, g, and h. b) Compare your resu to Prob 5. a) v b) The next figure is used for both problems 5 &6. It shows two masses mi and m, connected by a string...
How much rotational energy is stored in a 7.0 kg object being swung by a rope...
How much rotational energy is stored in a 7.0 kg object being swung by a rope in a 1.0 m radius circle at a rate of 2 revolutions per second?
2. A bar on a hinge starts from rest and rotates with an angular acceleration α...
2. A bar on a hinge starts from rest and rotates with an angular acceleration α (10 + 61), where α is in rad/s" and 1 is in seconds. Determine the angle in radians through which the bar turns in the first 4.00 s. 4. A dentist's drll starts from rest. After 3.20 s of constant an- gular acceleration, it turns at a rate of 2.51 × 104 rev/min. (a) Find the drill's angular acceleration. (b) Determine the angle (in...
03. For the system in Figure 3 where and are the rotational angles, /, and 2 are the rotary inertias of the two disks w...
03. For the system in Figure 3 where and are the rotational angles, /, and 2 are the rotary inertias of the two disks with radius r and 2r, respectively, (1) Find its total kinetic energy, total potential energy and e, 2r Lagrangian in terms of θ' and θ, (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and Im In 4) Calculate the natural frequencies and the associated mode...
The oxygen molecule, O2, has a total mass of 5.30×10-26 kg and a rotational inertia of...
The oxygen molecule, O2, has a total mass of 5.30×10-26 kg and a rotational inertia of 1.94×10-46kg-m2 about an axis perpendicular to the center of the line joining the atoms. Suppose that such a molecule in a gas has a speed of 1.48×102m/s and that its rotational kinetic energy is two-thirds (2/3) of its translational kinetic energy. Find its angular velocity.
A thin uniform rod (mass= 4.0 kg, length= 120.cm) rotates about an axis that is perpendicular...
A thin uniform rod (mass= 4.0 kg, length= 120.cm) rotates about an axis that is perpendicular to the rod; the axis intersects the rod at 1/3 of the rod's length. The rod rotates about the axis at the rate of 8 full revolutions per second. a. Compute the rotational Inertia of the rod based on the given axis of rotation. b. Compute the magnitude of the angular velocity in radians per second c. Compute the tangential speed of the end...
rods of negligible mass lying along the y axis connect three particles. The system rotates about the x axis with an angular peed of 3.70 rad/s. (a) Find the moment of inertia about the x axis. kg middot m^2 (b) Find the total rotational kinetic energy evaluated from 1/2 I omega^2. J (c) Find the tangential speed of each particle. 4.00 kg particle m/s 2.00 kg particle m/s 3.00 kg particle m/s (d) Find the total kinetic energy evaluated from...
Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of, and (2) Derive the equations of motion using Lagrangian equation method, (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode shapes if m-30 g, 4-8 x...
6. (20) Energy conservation analysis: Use conse frictional force, to directy find the kinetic energy of the sysin ysis: Use the conservation of energy, coupled with the work done by the when m2 hits the ground. With that ds a symbolic relation involving u, m, m2, g, and h. b) Compare your resu to Prob 5. a) v b) The next figure is used for both problems 5 &6. It shows two masses mi and m, connected by a string...
2. A bar on a hinge starts from rest and rotates with an angular acceleration α (10 + 61), where α is in rad/s" and 1 is in seconds. Determine the angle in radians through which the bar turns in the first 4.00 s. 4. A dentist's drll starts from rest. After 3.20 s of constant an- gular acceleration, it turns at a rate of 2.51 × 104 rev/min. (a) Find the drill's angular acceleration. (b) Determine the angle (in...
03. For the system in Figure 3 where and are the rotational angles, /, and 2 are the rotary inertias of the two disks with radius r and 2r, respectively, (1) Find its total kinetic energy, total potential energy and e, 2r Lagrangian in terms of θ' and θ, (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and Im In 4) Calculate the natural frequencies and the associated mode...
A thin uniform rod (mass= 4.0 kg, length= 120.cm) rotates about an axis that is perpendicular to the rod; the axis intersects the rod at 1/3 of the rod's length. The rod rotates about the axis at the rate of 8 full revolutions per second. a. Compute the rotational Inertia of the rod based on the given axis of rotation. b. Compute the magnitude of the angular velocity in radians per second c. Compute the tangential speed of the end...
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