Calculating the moment of inertia. Solution diagram provided in jpg format.

Find the moment of inertia of a thin sheet of mass M in the shape of an equilateral triangle about an axis through a vertex, perpendicular to the sheet. The length of each side is L.

Net torque causes angular acceleration of a cylinder caused by a descending mass.

Mass m= 8 kg is suspended from a cord which passes over a frictionless pulley then wraps tengentially on the surface of a uniform cylinder, mass M= 12 kg radius R = .66 m, on a plane inclined at angle b= 25 degrees from horizontal. As the suspended mass descends it gives angular acceleration A to the cylinder rolling it without slipping up the plane. See attachment #1 for picture showing parameters. a. Develop a relationship between acceleration am, of the descending mass, and the linear acceleration ac, of the c. m. of the cylinder up the plane. b. Find the accelerations am, of the descending mass, and the acceleration ac, of the c.m of the cylinder. c. Find the friction force F on th... click for more

Gravity forces and fields between two masses.

Assume the earth to be a uniform spherical planet, mass M= (5.98 E 24) kg. (The number, in scientific notation, means '5.98 times 10 to the 24') The earth's radius is R= (6.37 E 6) m. part a. Find the force of gravity between the earth and a spacecraft whose mass is m= 36000 kg, which is at height h= 520,000 m above the surface. part b. From the definition of gravity field of the earth at the spaceship's location as 'the force the earth exerts on the spaceship divided by the mass of the spaceship' find the earth's field at that location. part c. Find the distance from the center of the earth to a point in space where the earth's gravity field is 2.5 nt/kg.

Gravity field at points interior to a uniform spherical shell of mass

Show that the gravity field of a spherical shell of matter is zero at all points within it.

Pulley system

A disk of mass M and radius R unwinds from a tape wrapped around it. The tape passes over a frictionless pulley, and a mass m is suspended from the other end. Assume that the disk drops vertically. a) Relate the accelerations of m and the disk, a and A, respectively to the angular acceration of the disk. Ans clue- If A were to equal 2a, then angular acceleration would equal 3A/R b) Find a, A and angular acceleration