Auniform wheel of mass 12 kg and radius 0.4 m is mounted rigidly on a massless axle through its center. the radius of the axle is 0.2 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.6 kg m2 . the wheel is initially at rest at the top of a surface that is inclined at angle =30o with the horizontal. the axle rests on the surface while the wheel extends into a groove in the surface without touching the surface. once released, the axle rolls down along the surface without slipping. when the wheel-axle combination has moved down along the surface by 5 m, what is its center-of-mass velocity?

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

Aferris wheel is a vertical, circular amusement ride with radius 9 m. riders sit on seats that swivel to remain horizontal. the ferris wheel rotates at a constant rate, going around once in 9 s. consider a rider whose mass is 56 kg. at the bottom of the ride, what is the perpendicular component of the rate of change of the rider's momentum? at the bottom of the ride, what is the vector force exerted by the seat on the rider?

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) .