4.95m/s²
In rotational motion, the tangential acceleration ([tex]a_{t}[/tex]) is the product of the angular acceleration (∝) and the distance (r) from the axis of rotation and this is given by;
[tex]a_{t}[/tex] = ∝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;
[tex]a_{t}[/tex] = (ω/t)r ----------------(ii)
Now;
From the question;
ω = 100000rpm
Convert this to rad/s as follows;
ω = [tex]\frac{100000 * 2\pi }{60}[/tex] = 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 = [tex]\frac{8.50}{100}[/tex] = 0.085m
Substitute these values into equation (ii) as follows;
[tex]a_{t}[/tex] = (10473.3/180) (0.085)
[tex]a_{t}[/tex] = 4.95m/s²
Therefore, the tangential acceleration is 4.95m/s²
