13. Two particles (A and B) are Located at some distance from each other. Partic
ID: 1384668 • Letter: 1
Question
13. Two particles (A and B) are Located at some distance from each other. Particle A is twice as massive as particle B. A is held stationary while B is moved away at speed v. What happens to the center of mass of the two-particle system? a) it moves away from A with speed V b) it moves away from A with speed 2v c) it moves away from A with speed v/4 d) it moves away from A with speed v / 3 e) it moves away from A with speed 2v / 3 13. The inner hoop has twice the angular speed of the outer hoop and half the radius of the outer hoop. How do the centripetal accelerations of the hoops compare? 14. The angular speed of a propeller on an airplane decreased at a rate of -2.67 rad/s^2 for 12.0 s to obtain a final speed of 75 rad / s. What was the initial angular speed of the propeller? (a) 170 rad/s (b) 107 rad/s (c)43.0 rad/s (d) 188 rad/s 15. (a) For the previous problem, through what angle (in radians) did the propeller turn during the deceleration and (b) how many rotations is this (show your work)?Explanation / Answer
mass of A is M = 2m
Mass of B is m = m
Velocity of A is V = 0
Velocity of B is v = v
Velocity of center of mass = [ MV + m v ] / ( M + m)
= [ 0 + m v ) / ( 2m + m)
= mv / 3m
= v / 3
Option( d) is correct
(13) .Angular speed of outer hoop w = w
Angular speed of inner hoop W = 2w
Radius of outer hoop r = r
Radius of inner hoop R = r / 2
Centripetal accleration of outer hoop a o = rw 2
Centripetal accleration of inner hoop a i = RW 2
= ( r/2) (2w) 2
= 2 r w 2
Option ( b) is correct
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