Ring c has an inside radius of 55 mm and an outside radius of 60 mm and is positioned between two wheels a and b, each of 24-mm outside radius. knowing that wheel a rotates with a constant angular velocity of 300 rpm and that no slipping occurs, determine (a) the angular velocity of the ring c and of wheel b, (b) the acceleration of the points on a and b that are in contact with c.

In a thunderstorm, charge builds up on the water droplets or ice crystals in a cloud. thus, the charge can be considered to be distributed uniformly throughout the cloud. for the purposes of this problem, take the cloud to be a sphere of diameter 1.00 kilometer. the point of this problem is to estimate the maximum amount of charge that this cloud can contain, assuming that the charge builds up until the electric field at the surface of the cloud reaches the value at which the surrounding air breaks down. this breakdown means that the air becomes highly ionized, enabling it to conduct the charge from the cloud to the ground or another nearby cloud. the ionized air will then emit light due to the recombination of the electrons and atoms to form excited molecules that radiate light. in addition, the large current will heat up the air, resulting in its rapid expansion. these two phenomena account for the appearance of lightning and the sound of thunder. take the breakdown electric field of air to be eb=3.00ă—106n/c. part a estimate the total charge q on the cloud when the breakdown of the surrounding air is reached. express your answer numerically, to three significant figures, using ďµ0=8.85ă—10â’12c2/(nâ‹…m2) .

A30 kg weight lies on top of a massless piston of area a = 0.01 m2 the exterior air is at a (constant) p =1 atm and t = 27 c. the interior gas is 0.4 moles of (ideal) n2 and it has initial temperature 27.00 degrees c. 1. what is the initial pressure in the interior? a. 29.4 kpa b. 130.7 kpa c. 101.3 kpa the next three questions concern what happens when an amount of heat q is slowly added to the interior, raising the piston by 1 mm and raising the interior temperature to 27.40 c

Awind turbine is rotating counterclockwise at 0.5 rev/s and slows to a stop in 10 s. its blades are 20 m in length. (a) what is the angular acceleration of the turbine? (b) what is the centripetal acceleration of the tip of the blades at t=0s? (c) what is the magnitude and direction of the total linear acceleration of the tip of the blades at t=0s?