Consider a physical pendulum with length of 99.5 cm and mass of 185 g. if the pendulum was released from an angle less than 10°, then calculate the angular speed of the pendulum. (g = 9.80 m/s^2)

Two large, flat, horizontally oriented plates are parallel to each other, a distance d apart. half way betwween the two plates the electric field has magnitude e. if the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates?

The boy of mass 30 kg is at r1= 2 meters from the fulcrum. of the girl is 45 kg, at what r2 must she sit so that they are balanced ?

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)