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 ...continues

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 surfac ...continues

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 we ...continues

Marble rolling

A marble of mass M and radius R is rolled up a plane of angle A. If the initial velocity of the marble is Vo, what is the distance L it travels up the plane before it begins to roll back down? Ans clue: If Vo were to equal 3m/s, A=30, then l=1.3m

Yo-yo tension and force

A yo-yo of mass M has an axle of radius b and a spool of radius R. Its moment of inertia can be taken to be MR^2/2 and the thickness of the string can be neglected. The yo-yo is released from rest. a) What it the tension in the cord as the yo-yo descends and as it ascends? b)The center of the yo-yo descends distance h bef ...continues

Mass hitting a vertical plank

A plank of length 2l and mass M lies on a frictionless plane. A ball of mass m and speed Vo strikes its end (the plank is standing vertical and the ball strikes the top from the left). Find the final velocity of the ball, Vf, assuming that mechanical energy is conserved and that Vf is along the original line of motion. b)Fin ...continues

Central Force

A particle of mass 50g moves under an attractive central force of magnitude 4r^3 dynes. The angular momentum is equal to l,000 g*cm/s. a) Find the effective potential energy. b) Indicate on a sketch of the effective potential the total energy for circular motion. c) The radius of the particle's orbit varies between ro an ...continues

Central Force

A particle of mass 50g moves under an attractive central force of magnitude 4r^3 dynes. The angular momentum is equal to l,000 g*cm/s. a) Find the effective potential energy. b) Indicate on a sketch of the effective potential the total energy for circular motion. c) The radius of the particle's orbit varies between ro and 2ro. F ...continues