A 1380 kg car starts from rest at the top of a 28.0 m long hill inclined at 11.00 degrees. Ignoring friction, how fast is it going when it reaches the bottom of the hill?

Awind turbine is initially spinning at a constant angular speed. as the wind's strength gradually increases, the turbine experiences a constant angular acceleration 0.173 rad/s2. after making 2870 revolutions, its angular speed is 132 rad/s. (a) what is the initial angular velocity of the turbine? (b) how much time elapses while the turbine is speeding up?

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.

Ascientist notices that an oil slick floating on water when viewed from above has many different colors reflecting off the surface, making it look rainbow-like (an effect known as iridescence). she aims a spectrometer at a particular spot and measures the wavelength to be 750 nm (in air). the index of refraction of water is 1.3