Suppose a piece of dust finds itself on a cd. if the spin rate of the cd is 355 rpm, and the piece of dust is 4.5 cm from the center, what is the total distance (in m) traveled by the dust in 8 minutes? (ignore accelerations due to getting the cd rotating.) m

Aball is thrown upward in the air, and its height above the ground after t seconds is h ( t ) = 57 t − 16 t 2 feet. find the time t when the ball will be traveling upward at 14.25 feet per second.

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Acar moves a distance of 50.0 km west, followed by a distance of 64.9 km north what was the magnitude of the displacement of the car, in units of kilometers?