physics homework

Assignment #1: (Due Feb. 7) Vectors vs. Pseudovectors 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.) 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. 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 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. 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