Problem 2: Given a spinning disk with a straight slot as shown below. The slot is perpendicular to the radial direction and is at / fixed distance (( = 0) away from the disk center. Particle P is moving freely within the slot, its distance from the mid point is denoted as d (d / 0). Inertial frame e is given and point O is inertially fixed. The angle 0 is indicated between e, and the slot center line. d- P ezA b2 O e1 (a) A reference frame b with bi-b2-by is given. Frame b is fixed in the spinning disk with b, parallel to the slot center line. What would the angle be between e, and b,? Write outthe relation between frame e and frame b, i.e. similar to Problem 4 from Homework 2. One way is sufficient. (b) Write the position vector of particle ' in both b and e frame. Is there any choice of b frame that is more convenient than other choices? Give one example for an alternative disk-fixed frame (draw and define the frame only, no need to work position, velocity, or acceleration). (d) Find the velocity of particle as observed in the rotating b frame, ". Does your answer make sense? (e) Without assuming constant spin rate (0 * 0, 0 * 0), find the inertial velocity of particle (v"). You learned to take the derivatives when the position is expressed in e frame, but can you rewrite (simplify) your result using the frame conversion from part (a)? Does your result make sense? (f) Carry on differentiating to find the particle's inertial acceleration ("a"). Don't forget I is a constant distance (1 = 0), whereas d is not (d / 0, d / 0). Express "a" in by and b2