Please answer the question neatly with steps and show all units, for good rating

Question

Please answer the question neatly with steps and show all units, for good rating!

A record in an old record player starts from rest and accelerates to a final rotational velocity of 45 mevlmin in o.25sec. (an what is the rotational acceleration units? (b) What is the of the rotational distance traveled in this 0.25sec in rev and in radians?? (e) Where is the location 5,98 center of of the earth-moon system if the mass of the earth is k and the mass the moon is mass the earth to the moon is 3,86 x 10 m. (Express your x 1022kg and the distance from answer as a distance from the center of the earth. Note this part has no oonnection to parts and of this problem.)

Explanation / Answer

w0 = 0, w=45 rev/min = 45*60/2*pi rad/s=429.94rad/s

angular accleration,

alpha = (w0-w)/t

          = 429.94-0 /0.25 =1719.75 rad/s^2

angular distance

theta=theta0+1/2*alpha*t^2

         = 0 +1/2*1/2*1719.75*.25^2

        =107.48 radians.

For center of mass:

distance from earth x, from moon 3.86*10^8 - x

moment at this point is zero,

5.94*10^24*x = 7.38*10^22*(3.86*10^8 - x)

5.94*10^24*x +7.38*10^22x= 28.49*10^30

x =4.737*10^6 m

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