a) The initial angular speed is simply

`omega_0 = 2*pi*F =2*pi*3600 rad/min =2*pi*3600/60 (rad)/(sec)=`

` =120*pi (rad)/(sec) ~~377 (rad)/(sec)`

**The initial angular speed is `120*pi` rad/sec**

b)

The centrifuge does 50 complete rotations before it stops. One complete rotation means an angle of `2*pi` . The total angle of rotation is thus

`alpha =50*(2*pi) =100*pi =314.16 rad `

or `alpha =50*360 = 18000 degree`

**The total angle until stop is `100*pi` rad.**

c) The angular acceleration comes from

`omega^2 =omega_0^2 +2*epsilon*alpha`

(similar to `V^2 =V_0^2+2*a*s` )

`omega =0`and `omega_0 =377 (rad)/s` means

`epsilon = (omega^2-omega_0^2)/(2*alpha) =-377^2/(2*314.16) =-226.2 (rad)/s^2`

**The angular acceleration is `-226.2 (rad)/sec^2`**

d)

The time until stop comes from equation

`omega =omega_0 +epsilon*t` (similar `V=V_0 +a*t` )

`t = -omega_0/epsilon =377/226.2 =1.67 sec`

**The time until stop is 1.67 sec**

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