A boy and a girl are riding a merry- go-round which is turning ata constant rate. The boy is near the outer edge, while a girl is closer to the center. Who has the greater tangential acceleration? 1. the boy 2. the girl 3. both have zero tangential 25% try penalty acceleration Hints: 0,0 4. both have the same non-zero tangential acceleration

The correct answer is

1. the boy 2.

Explanation:

Since Tangential acceleration = v²/r  then the

v = ωr and v² =  ω²r² then the tangential acceleration = ω²r²/r = ω²r

This shows that  since ω is the same for both of them, the boy with greater r has the most acceleration.

The tangential acceleration α·r

true tan speed = ang vel x radius

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s