physics homework

Assignment #1: (Due Feb. 7)

1. Vectors vs. Pseudovectors

   1. Show that the vector cross product of two pseudovectors is a pseudovector and that the vector cross product of a vector and a pseudovector is a vector. (Recall that a pseudovector is defined as the result of the cross product of two vectors.)

   2. Consider the effect that a mirror operation on the components of a vector. Describe any differences between a vector and a pseudovector under the mirror operation.

2. Velocity and Acceleration

a. A body moving in a straight line with uniform acceleration passes two consecutive equal space, each of width w in times t and t . Show that the acceleration is: 2wt1  t2  .

3. RotationalMotion

a. A reel of thread whose rim and spindle are of radius a and b respectively rests of a rough horizontal table. The loose end of the thread passes under the spindle and leads off at an angle

 above the horizontal   12   . Show that the least tension in it will, in general, wind or unwind the tread according as is less or greater than a certain value. When has this critical

value, show that there will be no motion unless the tension exceeds another critical value.

4. Orbital Motion

1. A mass approaches the solar system with a velocity v0 , and if it had not been attracted toward

   the sun it would have missed the sun by a distance b . Use the laws of conservation of energy and angular momentum and the law of gravitation to compute its closest distance of approach

   a to the sun. Neglect the gravitational attractions of the planets and assume the sun is fixed.

2. Note, the answer is a  b2  b2 1/ 2  b where b  GM with M being the mass of the sun.

1 2 tt t t  1212

0 0 0 v02