Question

28. II A 4.0-m-diameter playground merry-go-round with a moment of inertia of 400 kg m2, is freely rotating with an angu- lar velocity of 2.0 rad/s. Ryan, whose mass is 80 kg, runs on the ground around the outer edge of the merry-go-round in the opposite direction to its rotation. Still moving, he jumps directly onto the rim of the merry-go-round, bringing it (and himself) to a halt. How fast was Ryan running when he jumped on? A. 2.0 m/s B. 4.0 m/s C. 5.0 m/s D. 7.5 m/s E. 10 m/s

Answer 1

Given radius of merry-go-round , r =2m

Moment of inertia of merry-go-round I_m= 400 kgm²

angular velocity of merry-go-round , $\omega _{m}$ = 2rad/s

mass of boy , m =80kg

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When the boy jumps on the rotating merry-go-round ,it stops

so Angular momentum of boy should be equal to that of merry-go-round

L_boy=L_m

$I_{boy}*\omega _{boy}=I_{m}\omega _{m}$

$mr^{2}*\omega _{boy}=400*2$

$mr^{2}*v/r=400*2$

$mr*v=800$

$v=800/()80*2)$

$v=5m/s$

ANSWER:Option C. 5.0m/s