A 0.772 kg glass jar falls off a shelf and reaches the ground with 11.2 J
of KE. How high was the shelf?
(Unit = m)

Awheel rotates without friction about a stationary horizontal axis at the center of the wheel. a constant tangential force equal to 82.0 n is applied to the rim of the wheel. the wheel has radius 0.150 m . starting from rest, the wheel has an angular speed of 12.8 rev/s after 3.88 s. what is the moment of inertia of the wheel?

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) .

Apotter's wheel moves uniformly from rest to an angular speed of 0.20 rev/s in 32.0 s. (a) find its angular acceleration in radians per second per second. rad/s2 (b) would doubling the angular acceleration during the given period have doubled final angular speed?