On what factor inertia of a body depends? Inertia depends on mass and density.

Awheelhas a radius of 4.8 m. howfar (path length) does a point on the circumference travel if thewheel is rotated through angles of 30°, 30 rad, and 30 rev,respectively?

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.

What do you think car designers do if the damage caused by a crash test is too severe?