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moment of inertia about center of mass and torque applied
189056 They rotate about the center of mass See the attached problem below.
A 0.9 kg mass at (x, y) = (20 cm, 20 cm) and a 2.6 kg mass at (20 cm, 100 cm) are connected by a massless, rigid rod. They rotate about the center of mass.
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Questions on Center of mass, Torque and Levers
352511 Questions on Center of mass, Torque and Levers Please refer to the attachment for the mentioned figures.
1.
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Torque, Equilibrium, and Stability
If the mass of the board is 15 kg, how close to the end can the painter stand without tipping the board over? Torque of board from scaffolding:
Center of board is center of mass which is 1.25m from scaffolding.
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Physical quantities of system of particlaes
The total energy of the system is simply:
The position of the center of mass is:
And the speed of the center of mass is:
Thus, the translational energy is:
The rotational energy is the difference between the total energy and
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Rotational Simple Harmonic Oscillation: Pivot for minimum
A disk of radius R is suspended from a pivot somewhere between its center and edge. Fow what pivot point will the period of this physical pendulum be a minimum?
Let the mass of the disk is m. and the pivot point is at a distance x from its center.
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Apply 'net torque = I alpha'; angular momentum for ratio of angular to initial velocity
Apply 'net torque= I alpha' to express the torque in terms of the moment of inertia and the angular velocity.
PART b. Example: A uniform thin ring, mass M, radius R, is rotating about an axis at its center with initial angular velocity.
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Torque, Equilibrium and Stability
The center of mass of the meter stick is in the center since it is uniform:
Ft (1.0m) = 5.0N(0.5m) + (0.15kg*9.8m/s^2)(0.75m)
Ft (1.0m) = 2.5Nm + 1.10Nm = 3.6nM
Therefore:
Ft = 3.6N Solution proceeds with trying to keep the system in equilibrium
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Torque, Equilibrium, & Stability
39446 Torque, Equilibrium, & Stability Two children are sitting on a seesaw. If one child has a mass of (m1) =22.0 kg and sits 2.30 m from the center pivot:
(a) How far from the pivot must the second child (m2) = 30.0 kg sit for them to balance?
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Torque, Static Equilibrium, and Rotational Dynamics.
117298 Torque, Static Equilibrium, and Rotational Dynamics A solid cylinder of mass 10 kg and radius 1 rn rotates with an angular speed of 10 rad / s about a vertical axis through its center.
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Rotation: Moment of inertia and angular velocity.
The rod is rotating cw about its center of mass at 20 rpm.
What torque will bring the balls to a halt in 5.0 s? in Nm
--- Please see the attached file. Four problems related to rotational motion are solved.