(a) The angular acceleration is given by:
[tex] \alpha=\frac{\omega_f-\omega_i}{\Delta t} [/tex]
where
[tex] \omega_f [/tex] is the final angular velocity
[tex] \omega_i [/tex] is the initial angular velocity
[tex] \Delta t [/tex] is the time interval
Let's convert the angular velocities in rad/s and the time in seconds:
[tex] \omega_f=100000 \frac{rev}{min}=100000 \frac{rev}{min} \frac{2 \pi rad/rev}{60 s/min}=10467 rad/s [/tex]
[tex] \omega_i=0 [/tex]
[tex] \Delta t=2.00 min \cdot 60 \frac{s}{min} = 120 s [/tex]
Substituting the numbers into the equation, we find the angular acceleration:
[tex] \alpha=\frac{10467 rad/s}{120 s}=87.2 rad/s^2 [/tex]
(b) The tangential acceleration is given by the product between the angular acceleration and the distance of the point from the axis of rotation. In this case, the distance is
[tex] r=9.5 cm=0.095 m [/tex]
Therefore the tangential acceleration is
[tex] a=\alpha r=(87.2 rad/s^2)(0.095 m)=8.3 m/s^2 [/tex]
(c) The radial acceleration (also known as centripetal acceleration) is given by the product between the square of the angular velocity and the distance from the axis of rotation:
[tex] a=\omega^2 r=(10467 rad/s)^2(0.095 m)=1.04 \cdot 10^7 m/s^2 [/tex]
