Ahoop is rolling without slipping along a horizontal surface with a forward speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. what is the speed of the hoop after it has rolled 3.00 m up as measured along the surface of the ramp

(**i would really appreciate if this was answered soon** ) which pair of quantities includes one quantity that increases as the other decreases during simple harmonic motion?

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 discovery of the electron as a subatomic particle was a result of