A merry-go-round with a a radius of R = 1.74 m and moment of inertia I = 181 kg-

Question

A merry-go-round with a a radius of R = 1.74 m and moment of inertia I = 181 kg-m2 is spinning with an initial angular speed of ? = 1.69 rad/s in the counter clockwise direection when viewed from above. A person with mass m = 70 kg and velocity v = 4.3 m/s runs on a path tangent to the merry-go-round. Once at the merry-go-round the person jumps on and holds on to the rim of the merry-go-round.

1)

What is the magnitude of the initial angular momentum of the merry-go-round?

kg-m2/s

2)

What is the magnitude of the angular momentum of the person 2 meters before she jumps on the merry-go-round?

kg-m2/s

3)

What is the magnitude of the angular momentum of the person just before she jumps on to the merry-go-round?

kg-m2/s

4)

What is the angular speed of the merry-go-round after the person jumps on?

rad/s

5)

Once the merry-go-round travels at this new angular speed, with what force does the person need to hold on?

N

6)

Once the person gets half way around, they decide to simply let go of the merry-go-round to exit the ride.

What is the magnitude of the linear velocity of the person right as they leave the merry-go-round?

m/s

7)

What is the angular speed of the merry-go-round after the person lets go?

rad/s

(Survey Question)

Explanation / Answer

1)magnitude of the initial angular momentum of the merry-go-round L = I*w..
L1 = I*w = 181*1.69 = 305.89 kg-m2/s
2)L2 = m*v*r*sin(theta)....
theta = 90 degrees because the person was moving tangentially..
L2 = m*v*r = 70*4.3*1.74 = 523.74 kg-m2/s

3)L3 = m*v*r*sin(theta)....
theta = 90 degrees because the person was moving tangentially..
L3 = m*v*r = 70*4.3*1.74 = 523.74 kg-m2/s...

4)L1+L2 = (I1+I2)*wf...
given I1 = 181 kg-m^2.
I2 = m*R^2 = 70*1.74^2 = 211.932 kg.m^2
wf = (L1+L2)/(I1+I2) =
wf= (305.89+523.74)/(181+211.932) = 2.12rad/s

5) F = m*v^2/r = m*r2*wf^2

F= 70*1.74*2.12^2 = 542.98 N

6) v = r*wf = 3.688 m/sec...

7)L1+L2 = I1*wf...
I1 = 181 kg-m^2.
wf = (L1+L2)/I1 = (305.89+523.74)/(181)= 4.58 rad.sec

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