circular motion

Question

An ultracentrifuge accelerates from rest to 98300 rpm in 1.85 min.

ω = 98300 rpm

t = 1.85 min

l = 9.9 cm

a) what is the angular acceleration in rad/s²?

b) what is the tangential acceleration of a point 9.9 cm from the axis of rotation in m/s^2?

c) what is the centripetal acceleration in multiples of g of this point at full speed?

Answer 1

a) 2 pi radians / rev. x 98300 revs. /min. x 1 min. / 60 sec = 1.029 x 10^4 rad/sec

angular acceleration = (V_final - V_initial ) / time(sec)

= (1.029 x 10^4 rad/sec - 0 ) / 1.85 min x 60 sec / min = 92.7 rad/s^2

b) angular acceleration = tangential acceleration / radius

tangential accel. = radius (m) x angular acceleration = 0.099 m x 92.7 rad/s^2 = 9.2 m/s^2

c) centripetal acceleration = angular velocity^2 x radius

centripetal acceleration = (1.029 x 10^4 rad/s)^2 x 0.099 m = 1.1 x 10^9 m/s^2

In units of g, 1.1 x 10^9 / 9.8 = 1.1 x 10^8 g

Always check the math.