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EXERCISE 7.65 A known couple?(t) induces rotation of the system about the vertical axis. Collars A...
Problem Consider the uniform bar of in the igure below. A&T 9 Axis of rotation: O...
Problem Consider the uniform bar of in the igure below. A&T 9 Axis of rotation: O moment of inertia of the bar about the axis of rotation, o, is-mL, whe m is the mass of the bar and L is the length. Derive the differential equation representing the rotational motion of the bar. That is, find the equation of motion. (15 pts) The Page 8 of 8
To apply the equations of motion to a system that involves rotation about a fixed axis...
To apply the equations of motion to a system that involves
rotation about a fixed axis and to use this information to
determine key characteristics.
The slender rod ABAB shown has a mass of m=51.0m=51.0 kgkg and
is being supported by a rope and pulley system stationed at CC.
Starting from rest (in the position shown), the rope and pulley
system tug on the rod causing it to rotate about AA. The torque
applied to the pulley is T=2.85T=2.85 kN⋅mkN⋅m...
PROBLEM -2 An Inertia J of radius r attached to a fixed axis of rotation A as shown below. The inertia is in contac...
PROBLEM -2 An Inertia J of radius r attached to a fixed axis of rotation A as shown below. The inertia is in contact with a mass M attached via aspring of stiffness K to a fixed wall. The inertla- mass contact is subject to viscous friction of coefficient f. The motion of the mass with respect to the horlzontal floor is subject to the same viscous friction coefficient f..The system input is a horizontal force f(t) on the mass...
Learning Goal: To apply the equations of motion to a system that involves rotation about a...
Learning Goal:
To apply the equations of motion to a system that involves
rotation about a fixed axis and to use this information to
determine key characteristics.
The slender rod ABAB shown has a mass of m=53.0m=53.0 kgkg and
is being supported by a rope and pulley system stationed at CC.
Starting from rest (in the position shown), the rope and pulley
system tug on the rod causing it to rotate about AA. The torque
applied to the pulley is...
Question 5 (20 marks) a) Develop a Lagrangian for the system shown, for small displacements from equilibrium when 6 (t)-0. The cylinder rotates on a fixed axis and has moment of inertia, J, about thi...
Question 5 (20 marks) a) Develop a Lagrangian for the system shown, for small displacements from equilibrium when 6 (t)-0. The cylinder rotates on a fixed axis and has moment of inertia, J, about this axis. [5 marks] x (t) k2 b) Then use Lagrange's Equation to determine the equations of motion. M(t) denotes an external moment applied to the cylinder. Also, express the equations in matrix form. [10 marks] c) Comment briefly on the dominant dynamic effects you would...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
EXERCISE 3.28 The entire system rotates about the vertical axis at constant angular speed , and...
EXERCISE 3.28 The entire system rotates about the vertical axis at constant angular speed , and the rotation rate 2 of the ro- tor relative to bar BC also is constant. (a) Describe the angular velocity of the rotor in terms of a superposition of simple rota- tions. (b) Solely from an examination of the description in Part (a), predict the direction(s) in which the angular acceleration of the rotor will be situated relative to the xyz axes defined in...
A uniform rod rotates in a horizontal plane about a vertical axis through one end. The...
A uniform rod rotates in a horizontal plane about a vertical
axis through one end. The rod is 12.00 m long, weighs
20.00 N, and rotates at 350 rev/min clockwise when seen
from above. Calculate its rotational inertia about the axis of
rotation.
Tries 0/5
Calculate the angular momentum of the rod about that axis.
A man stands at the center of a platform that rotates without
friction with an angular speed of 1.2 rev/s. His arms are
outstretched, and...
Problem Consider the uniform bar of in the igure below. A&T 9 Axis of rotation: O moment of inertia of the bar about the axis of rotation, o, is-mL, whe m is the mass of the bar and L is the length. Derive the differential equation representing the rotational motion of the bar. That is, find the equation of motion. (15 pts) The Page 8 of 8
To apply the equations of motion to a system that involves
rotation about a fixed axis and to use this information to
determine key characteristics.
The slender rod ABAB shown has a mass of m=51.0m=51.0 kgkg and
is being supported by a rope and pulley system stationed at CC.
Starting from rest (in the position shown), the rope and pulley
system tug on the rod causing it to rotate about AA. The torque
applied to the pulley is T=2.85T=2.85 kN⋅mkN⋅m...
PROBLEM -2 An Inertia J of radius r attached to a fixed axis of rotation A as shown below. The inertia is in contact with a mass M attached via aspring of stiffness K to a fixed wall. The inertla- mass contact is subject to viscous friction of coefficient f. The motion of the mass with respect to the horlzontal floor is subject to the same viscous friction coefficient f..The system input is a horizontal force f(t) on the mass...
Learning Goal:
To apply the equations of motion to a system that involves
rotation about a fixed axis and to use this information to
determine key characteristics.
The slender rod ABAB shown has a mass of m=53.0m=53.0 kgkg and
is being supported by a rope and pulley system stationed at CC.
Starting from rest (in the position shown), the rope and pulley
system tug on the rod causing it to rotate about AA. The torque
applied to the pulley is...
Question 5 (20 marks) a) Develop a Lagrangian for the system shown, for small displacements from equilibrium when 6 (t)-0. The cylinder rotates on a fixed axis and has moment of inertia, J, about this axis. [5 marks] x (t) k2 b) Then use Lagrange's Equation to determine the equations of motion. M(t) denotes an external moment applied to the cylinder. Also, express the equations in matrix form. [10 marks] c) Comment briefly on the dominant dynamic effects you would...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
EXERCISE 3.28 The entire system rotates about the vertical axis at constant angular speed , and the rotation rate 2 of the ro- tor relative to bar BC also is constant. (a) Describe the angular velocity of the rotor in terms of a superposition of simple rota- tions. (b) Solely from an examination of the description in Part (a), predict the direction(s) in which the angular acceleration of the rotor will be situated relative to the xyz axes defined in...
A uniform rod rotates in a horizontal plane about a vertical
axis through one end. The rod is 12.00 m long, weighs
20.00 N, and rotates at 350 rev/min clockwise when seen
from above. Calculate its rotational inertia about the axis of
rotation.
Tries 0/5
Calculate the angular momentum of the rod about that axis.
A man stands at the center of a platform that rotates without
friction with an angular speed of 1.2 rev/s. His arms are
outstretched, and...
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