Cosmic Rays Protons in cosmic rays have been observed with kinetic energies as large as . (a) How fast are these protons moving? Give your answer as a fraction of the speed of light. (b)Show that the kinetic energy of a single one of these protons is much greater than the kinetic energy of a 15-mg ant walking with a speed of 8.8 mm/s.

Lectures 6 a nd 7 Relative Motion Motion from other p erspectives Uniform Circular Motion Speed is fixed Velocity and acceleration n ot 0 Directionally changing velocity Acceleration called “radial or centripetal” acceleration EQUATION a = v 2 c r Time it takes to complete one revolution is one “period”, T (in seconds) EQUATION v = 2πr = 1 circumference T 1 period Rotational (Angular) Rotation θis ositive g oing counterclockwise f rom p ositive xaxis (x,y) or (r, θ s coordinates arc length