Moment of Inertia of a Uniform cylinder about an axis at center perpendicular to its face.

Moment of inertia problem A uniform cylinder has mass M and radius R. a. Find by integration the moment of inertia, Io, about its center of mass axis at center, perpendicular to the face of the cylinder. b. Use the translation of axis theorem, 'Ip = Io + M h^2' to find the moment of inertia about an axis parallel to that above, through a point on the rim of the cylinder.

Scattering angle

Particle A of mass m has initial velocity Vo. After colliding with particle b of mass 2m initially at rest, the particles separate. Particle b has a scattering angle of 45 degrees and Particle a has a final velocity of Vo/2. Find the scattering angle of particle A.

'Net torque equals I alpha' As mass m descends it rotates the cylinder with angular acceleration.

A uniform cylinder, mass M= 25 kg, radius R= .75 m, is mounted on a fixed, frictionless bearing. From a cord wrapped on its surface a mass m=6.4 kg descends and rotates the cylinder with angular acceleration 'A'. See attachment for picture of the apparatus. a. Find the angular acceleration of the cylinder. b. Find the tension, C, in the cord.

Helium balloon acceleration with load

Balloons are often filled with helium gas because it weighs only about one-seventh of what air weighs under identical conditions. The buoyancy force which can be expressed as Fb = (density of air)(g)(volume of balloon), will push the balloon upward. If the balloon has a diameter of 14.0 m, may be treated as spherical, and carries 6 passengers, each of mass 72.5 kg, determine the acceleration of the balloon when it is first released. Assume that the density of air is 1.16 kg/m3 , and neglect the weight of the ropes and basket.

Calculating a change in temperature given power, density, mass, dimensions, and specific heat capacities.

A class of 12 students taking an exam has a power output per student of 126 W. Assume that the initial temperature of the room is 19.5°C and that its dimensions are 6.20 m by 14.4 m by 3.30 m. What is the temperature (in °C, do not enter units) of the room at the end of 63.0 min if all the heat remains in the air in the room and none is added by an outside source? The specific heat of air is 831 J/ kg*°C, and its density is about 1.31à—10-3g/ cm3.