Question

A disk-shaped grindstone of mass 1.7 kg and radius 8 cm is spinning at 730 rev/min. After the power is shut off, a woman continues to sharpen her ax by holding it against the grindstone for 9 s until the grindstone stops rotating.
(a)What is the angular acceleration of the grindstone?
(b) What is the torque exerted by the ax on the grindstone? (Assume constant angular acceleration and a lack of other frictional torques.)

Answer 1

Answer:

0.186 N-m        

Explanation:

mass of the grindstone, $m=1.7 kg$

radius, $r=8 cm$

Frequency, $f=730 rev/min = 12.16 rev/s$

time, $t=9s$

final angular velocity, $\omega=0$

Initial angular velocity,

$\omega_o=2\pi f\\=2\pi (12.16) rad/s\\= 76.36 rad/s$

Angular acceleration of the grind stone is:

$\alpha=\frac{\omega-\omega_o}{t}\\\Rightarrow \alpha =\frac{0-76.36}{9} = -8.48 rad/s^2$

Moment of inertia:

$I=mr^2+mr^2=2mr^2$

$I=2\times 1.7 kg\times (0.08m)^2= 0.022kg-m^2$

Torque exerted by the ax on the grind stone is:

$\tau=I\alpha\\\tau=0.022\times (-8.48) \\\tau=0.186N-m$