Classical Mechanics Answers

Calculate the moment of inertia of the following figures: cone of the basic radius R and mass m.

In all cases you should use I = (x 2 +y 2 ) dV (dV = dx·dy·dz)

Hint (for simplicity):

Calculate the moment of inertia of the following figures: thick-walled cylinder of the outer and the inner radii R and r

respectively, and mass m;

Calculate the moment of inertia of the following figures: thin-walled cylinder of the radius R and mass m;

Calculate the moment of inertia of the following figures: in case B consider the problem in cylindrical

(dV=r·dr·dφ·dz) coordinate system.

Calculate the moment of inertia of the following figures:thick-walled sphere of the outer and the inner radii R and r

respectively, and mass m;

Calculate the moment of inertia of the following figures: solid ball of the radius R and mass m;

A tire has a tread pattern with a crevice every 2.00cm. Each crevice makes a single vibration as the tire moves.

a. what is the frequency of these vibrations if the car moves at 30m/s?

b. what is the period of vibration at the same speed?

c. what is the angular speed of the tire?

The measurements collected by the first year students:

displacement (m) 0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2

time (s) 0, 1.35, 2.82, 3.36, 4.64, 5.21, 6.89

With the given information above:

a. draw three graphs for distance versus time, speed versus time and acceleration versus time.

b. find the equation of the velocity time graph

 A puck with a mass of 0.170kg has velocity of +90km/H. The momentum of the puck is ??

A 360 kg roller coaster car traveling at 18 m/s collides inelastically with a stationary 240 kg car on a section of a horizontal track. To what maximum height, h, do the combined cars travel before rolling back down the hill?