Consider a solid cone with uniform density \rho, height h, and circular base with radius r (mass hr ). let the vertex of the cone be the origin of the body frame. by symmetry, choose basis vectors \mathbf{e}_{i} for the body frame such that the inertia tensor i_{ij} is diagonal.
(a) will this rigid body with this body origin be an asymmetric top, a symmetric top, or a spherical top? calculate the inertia tensor in this basis.
(b) how will the inertia tensor change if we change the body origin to the center of mass while the basis vectors remain fixed? hint: steiner’s parallel axis theorem might with this part of the problem.

Aknife blade is a(n) a. lever b. screw c. wedge d. inclined plane

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.

It can take some of those large , industrial vehicles up to feet to stop when traveling only 60 mph, and therefore , you shoukd be mindful to not be jn the traffic right in front of them a. 100 feet b. 200 feet c. 335 feet d. 425 feet