Why do we have dreams?

An isotope undergoes radioactive decay by emitting radiation that has a –1 charge. what other characteristic does the radiation have?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

The particle p starts from rest at point a at time t = 0 and changes its speed thereafter at a constant rate of 2.8g as it follows the horizontal path shown. determine the magnitude and direction of its total acceleration (a) just before point b, (b) just after point b, and (c) as it passes point c. state your directions relative to the x-axis shown (ccw positive) and choose the angle with the smallest magnitude.