
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.

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.

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.

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

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.

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.

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

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?

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.

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.