Ihave three, three dimensional, vectors r and f and v. the vector r is the displace- ment of an object of mass, m 5kg, from an axis of rotation that passes through the origin. the vector r lies in the z-y plane. has a length r = 4m and makes an angle with respect to the x-axis of 30 d i(1,3,-2 the vector f represents a force of 5 newtons, directed in the direction n-(1-1.-1) egrees. the mass, m, has a velocity (a) calculate the components of the vector r (b) what are the magnitude and direction of the angular momentum of our object? (c) use the dot product to determine the angle between the vectors r and f. (d) what is the magnitude of the torque about the axis at the origin that the force (e) use the expression for the cross product in terms of the components of the (f) does the magnitude of the vector calculated in part (e) agree with the results (g) find the unit vector that points in the direction of the torque calaculated in f exerts on the object at the position r? vectors to find the torque, = r × f. of part (d)? part (f)

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) .

A2-kg bowling ball is 2.5 meters off the ground on a post when it falls. just before it reaches the ground, it is traveling 7 m/s. assuming that there is no air resistance, which statement is true?

The speed of sound in ice, water, and steam is shown. what best explains the speed of sound in different states of matter? sound travels fastest in ice because energy is easier to transfer when the molecules are close together. sound travels slowest in steam because the sound has to move around the gas molecules that are far apart. sound travels fastest in ice because the temperature of solids is always greater, so the heat transfers the sound energy. sound travels slowest in steam because the pressure is so great the sound cannot travel though the steam particles.