A person with mass mp -79 kg stands on a spinning platform disk with a radius of

Question

A person with mass mp -79 kg stands on a spinning platform disk with a radius of R - 1.89 m and mass md - 184 kg. The disk is initially spinning at = 1.8 rad/s. The person then walks 2/ 3 of the way toward the center of the disk (ending 0.63 m from the center) 1) What is the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk? 610 kg-m2 Submit Your submissions: 610 Computed value: 610 Feedback: Correct! Submitted: Wednesday, November 1 at 8:44 PM 2) What is the total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk? 329.0301 kg-m2 Submit Your submissions: 329.0301 x Computed value: 329.0301 Feedbak: Submitted: Wednesday, November 1 at 9:08 PM 3) What is the final angular velocity of the disk? rad/s Submit 4) What is the change in the total kinetic energy of the person and disk? (A positive value means the energy increased.) J Submit 5) What is the centripetal acceleration of the person when she is at R/3?

Explanation / Answer

Given,

mp = 79 kg ; R = 1.89 m ; md = 184 kg ; w = 1.8 rad/s ;

1)The total moment of inertia of the person and disk system would be:

I0 = 1/2 md R^2 + mp R^2

I0 = 1/2 x 184 x 1.89^2 + 79 x 1.89^2 = 610.83kg-m^2

Hence, I0 = 610.83 kg-m^2

2)The moment of inertia now will be:

I1 = 1/2 md R^2 + mp (R/3)^2

I1 = R^2 ( md/2 + mp/9 )

I1 = 1.89^2 ( 184/2 + 79/9) = 360 kg-m^2

Hence, I1 = 360 kg-m^2

3)we know that angular momentum is conserved.

Lf = Li

I1 omega1 = Io omega0

omega1 = I0/I1 x omega0 = 610.83/360 x 1.8 = 3.1 rad/s

hence, omega1 = 3.1 rad/s

4)The intial and final KE of the system will be

KEi = 1/2 I0 omega0^2

KEi = 0.5 x 610 x 1.8^2 = 988.2 J

KEf = 0.5 x 360 x 3.1^2 = 1729.8 J

Change in energy will be:

Delta KE = KEf - Kei = 1729.8 - 988.2

Delta KE = 741.6 J

5)a = w^2 R

a = 3.1^2 x 1.89 = 18.16 m/s^2

Hence, 18.16 m/s^2

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