The tub of a washer goes into its spin-dry cycle, starting from rest and reaching an angular speed of 2.0 rev/s in 11.0 s. at this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. the tub slows to rest in 9.0 s. through how many revolutions does the tub turn during this 20 s interval? assume constant angular acceleration while it is starting and stopping.

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.

Alfred pushes on a heavy box, but cannot move it. the box has a lot of inertia motion friction gravity

Aball has an initial velocity of 3 m/s. if there is no friction, what is the highest it could roll?