A uniform solid cylinder of radius r and mass m can roll inside a hollow cylinder of radius R > r without slipping. A pendulum of length l = R−r 2 and mass M = m/2 is attached to the center of the smaller cylinder. Find the normal frequencies and normal modes of this system.

The mass of the sun is 1.99×1030kg and its distance to the earth is 1.50×1011m. what is the gravitational force of the sun on the earth?

Amichelson interferometer operating at a 600 nm wavelength has a 3.02-cm-long glass cell in one arm. to begin, the air is pumped out of the cell and mirror m2 is adjusted to produce a bright spot at the center of the interference pattern. then a valve is opened and air is slowly admitted into the cell. the index of refraction of air at 1.00 atm pressure is 1.00028.how many bright-dark-bright fringe shifts are observed as the cell fills with air?

Arefrigerator uses r-134a as the working fluid and operates on the ideal vapor-compression refrigeration cycle except for the compression process. the refrigerant enters the evaporator at 120 kpa with a quality of 34 percent and leaves the compressor at 70°c. if the compressor consumes 450 w of power, determine (a) the mass flow rate of the refrigerant, (b) the condenser pressure, and (c) the cop of the refrigerator. (0.00644 kg/s, 800 kpa, 2.03)