Question

A centrifuge in a medical laboratory rotates at an angular speed of 3,450 rev/min. When switched off, it rotates through 54.0 revolutions before coming to rest. Find the constant angular acceleration (in rad/s2) of the centrifuge. rad/s2

Answer 1

Lets imagine that the centrifuge is in circular shape and it is rotating in a counter clock wise direction. its initial angular velocity is given as 3450 rev/sec ( we need to convert this into radian/s) and it finally comes to rest so final angular velocity can taken as zero.

it also does 54 rev before coming to rest so angular displacement is 54 rev ( again, we need to convert it into radian )

lets solve it using angular kinematics-

I w;= 3450 rev/min min Initial & Wi= 3450 nev/min angular wooty : 3460 meu came overse) = 361 rad cappoox.) final angular & wf = 0 rad/sec. nelocity Augular displacement - 54 rev. = 54 ( 2 ) a 108 Radian. Using , Angular kinematics equation- wf² = wp²+ 200 Il new a. a = wf?- w; 2 20 - O? – (361) 2 x 108 t = = 192 rad 182 Au.

Alpha = Angular acceleration = -192 rad/s² .

angular acceleration is negative because its actually disacceleration ( rev/min is decreasing with time and finally being zero ).

Thank you.