Question

An ultracentrifuge accelerates from rest to 9.91×105 rpm9.91×105 rpm in 1.99 min1.99 min. What is its angular acceleration in radians per second squared?

angular acceleration:

rad/s2rad/s2

What is the tangential acceleration of a point 9.70 cm9.70 cm from the axis of rotation?

tangential acceleration:

m/s2m/s2

What is the radial acceleration in meters per second squared and in multiples of gg of this point at full revolutions per minute?

radial acceleration:

m/s2m/s2

radial acceleration in multiples of gg:

Answer 1

here,

a)

the initial angular velocity , w0 = 0 rad/s

the final angular velocity , w = 9.91 * 10^5 rpm

w = 1.04 * 10^5 rad/s

time taken , t = 1.99 min = 119.4 s

let the angular acceleration be alpha

using first equation of motion

w = w0 + alpha * t

1.04 * 10^5 = 0 + alpha * 119.4

solving for alpha

alpha = 871 rad/s^2

the angular acceleration is 871 rad/s^2

r = 9.7 cm = 0.097 m

the tangential acceleration , at = 0.097 * 871 m/s^2

at = 84.5 rad/s^2

the radial acceleration , ar = w^2 * r

ar = 84.5^2 * 0.097 m/s^2

ar = 692 m/s^2

ar = 692 /9.81 g = 70.6 g