Calculating the center of mass of a cylinder.

Determine the position of the center of mass of a thin parabolical shell defined by z = a^2 - r^2 in cylindrical polar coordinates, glued to a flat bottom where z = 0, r < a of the same thickness.

Projectile problem A marble fired from a roof at a known angle. Location of origin and impact point known.

A marble is fired at angle +30° from a roof top x,y origin 50 m above ground with velocity such that it falls into a bowl on the ground at (218, -50). a. Find the original speed Vo. b. Find the total time of flight of the marble. See diagram attachment for picture showing known data.

Potential Stablitiy

Determine when a solid shape produced by gluing a cylinder of height H and radius R to a hemisphere of radius R made from the same material will be in a stable equilibrium standing on its top. Note that the top is the hemishpere: therefore the hemisphere is the only part touching the ground.

Equilibrium with torques on a cylinder on an inclined plane

A unifom cylinder, mass M= 15 kg, rests on a plane inclined at angle b=30°, held stationary by a cord attached to the plane at angle a= 50° which applies tangential force C to the cylinder. A mass m= 5 kg is suspended on a cable which is wrapped on the surface of the cyiinder. The radius R is unknown. See the attachment for a diagram with all knowns. a. Find the force C in the cord. b. Find the friction force at the cylinder/plane contact.

Calculating the frequency of a tuning fork. A diagram of the setup is provided in jpg format.

A tuning fork is set into vibration above a vertical open tube filled with water. Please see the figure attached. The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is L1 = 0.180 m and L2 = 0.420 m. What is the frequency of the tuning fork? Note: The resonance at L1 is not necessarily the first harmonic or fundamental. However, the second resonance at L2 is the next harmonic after the harmonic at L1.