If, as soon as the angular speed is ω = 32 rad/s, the force is immediately removed and a mass m = 1.3 kg is dropped at r = 0.25 m on the disc and sticks there, what would be the new rotational velocity of the disc in rad/s?

The image shows the positions of a car on a roller coaster track. arrange the cars in order based on their gravitational potential energy. begin with the lowest potential energy and end with the highest.

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?