You may consult with your neighbors as you do this quiz. When done, fold your pa

Question

You may consult with your neighbors as you do this quiz. When done, fold your paper in half along a vertical line down the middle of the paper, and then pass to the center aisle. The diagram at the right show's a flat disk that is spinning. The disk has a mass of 2.0 kg and a diameter of 1.0 m. Near the edge sits a point mass of 100 grams. If the coefficient of static friction between the point mass and the disk is 0.5. what is the maximum angular velocity of the disk just before the point mass slides off the spinning disk? What is the total rotational inertia of the disk and the point mass? What is the total kinetic energy of the disk and point mass at the angular velocity in Find the gravitational force between the disk and the point mass?

Explanation / Answer

Mass of disk =m1=2kg

Mass of a point = m2 =100gm =0.1 kg

Diameter=1m

Radius of disk= 0.5 m

µs =0.5

Solution =

a)µs = F/N

µs =F/m2g

F = µs m2g

F= 0.5 *0.1 * 9.8

F= 0.49N

F= mv2/r

V2= Fr/m2

V2= 0.49 * 0.5/0.1

V2= 24.5m/s

V= 4.949m/s

V=r

=V/r

=4.949/0.5

angular velocity= =9.8995rad/s

b) Total rotational inertia=

I=1/2m1r2 +m2r2

I= 1/2(m1+m2)r2

I= (1+0.1) *0.52/2

I=0.1375kgm2

c)Total K.E.= ½ m1v2 + ½ m2v2

                      =½(m1+m2)v2

                       =1/2(1+0.1) 24.5

                        =13.475J

d) Gravitational force=

F= G m1m2/r2

=(6.673*10-11 *1*0.1)/0.52

F =2.6692*10-11 N

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