An ultracentrifuge accelerates from rest to 100,000 rpm in 3.00 min. What is the tangential acceleration of a point 8.50 cm from the axis of rotation

4.95m/s²

In rotational motion, the tangential acceleration () is the product of the angular acceleration (∝) and the distance (r) from the axis of rotation and this is given by;

= ∝r       ------------------(i)

But the angular acceleration (∝) is the ratio of the angular velocity(ω) to time (t). i.e

∝ = ω / t

Substitute this into equation (i) as follows;

= (ω/t)r         ----------------(ii)

Now;

From the question;

ω = 100000rpm

     Convert this to rad/s as follows;

     ω = = 10473.3rad/s

t = 3.00min

      Convert this to seconds as follows;

      t = 3.00 x 60s = 180.0s

r = 8.50cm

     Convert this to metres as follows

     r = = 0.085m

Substitute these values into equation (ii) as follows;

= (10473.3/180) (0.085)

= 4.95m/s²

Therefore, the tangential acceleration is 4.95m/s²

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