The particle p is released at time t = 0 from the position r = r0 inside the smooth tube with no velocity relative to the tube, which is driven at the constant angular velocity ω0 about a vertical axis. determine the radial velocity vr, the radial position r, and the transverse velocity vθ as functions of time t. explain why the radial velocity increases with time in the absence of radial forces. plot the absolute path of the particle during the time it is inside the tube for r0 = 0.19 m, l = 1.4 m, and ω0 = 1.29 rad/s. then answer the questions using the given numbers.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.

Alinear relationship would look like a straight line on the graph. it could have a positive negative or 0 slope. so it could be a line potentially going in any direction but it must be perfectly straight.

Simple harmonic motion wind energy circulation best answer from the choices