A pendulum is suspended from the cusp of a cycloid cut in rigid support. The path described by the pendulum bob is cycloidal and is given by: x = a (φ − sin φ) y = a(cos φ − 1), where the length of the pendulum is l = 4a, and where φ is the angle of rotation of the circle generating the cycloid. Shat that the oscillations are exactly isosynchronous with frequency ω0 = p g/l, independent of the amplitude.

Which energy transformation occurs in the core of a nuclear reactor? nuclear energy mechanical energy nuclear energy - thermal energy thermal energy -- nuclear energy mechanical energy - nuclear energy

Very large accelerations can injure the body, especially if they last for a considerable length of time. one model used to gauge the likelihood of injury is the severity index ( ), defined as =/ . in the expression, is the duration of the accleration, but is not equal to the acceleration. rather, is a dimensionless constant that = the number of multiples of that the acceleration is equal to. in one set of studies of rear-end collisions, a person's velocity increases by 13.7 km/h with an acceleration of 36.0 m/s2 . let the + direction point in the direction the car is traveling. what is the severity index for the collision?

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)