Types of Acceleration in Rotation Video Lessons

Concept

# Problem: An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in rad/s2 ?(b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation?(c) What is the centripetal acceleration in m/s2 and multiples of g of this point at full rpm?(d) What is the total distance traveled by point 9.5 cm from the axis of rotation of the ultracentrifuge?

###### FREE Expert Solution

Rotational kinematic equations:

Tangential acceleration:

$\overline{){{\mathbf{a}}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{\alpha }}{\mathbf{r}}}$

Centripetal acceleration:

$\overline{){{\mathbf{a}}}_{{\mathbf{c}}}{\mathbf{=}}{{\mathbf{\omega }}}^{{\mathbf{2}}}{\mathbf{r}}}$

(a)

First, we'll convert the angular velocity to rad/s.

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###### Problem Details

An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min.

(a) What is the average angular acceleration in rad/s2 ?

(b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation?

(c) What is the centripetal acceleration in m/s2 and multiples of g of this point at full rpm?

(d) What is the total distance traveled by point 9.5 cm from the axis of rotation of the ultracentrifuge?