Answer :
Final answer:
The force exerted at the edge of the solid disc grindstone creates torque which causes it to rotate with an angular acceleration. The torque can be calculated by multiplying force by radius, and the angular acceleration is obtained by dividing this torque by the moment of inertia of the disc.
Explanation:
In physics, the force applied to an object in a tangential direction with respect to a pivot point (which is the center in case of a circular grindstone) creates torque.
In this case, a force of 165 Newtons is being applied to the edge of the solid disc grindstone. The distance from the pivot point, i.e., the radius, is 1.6m. Torque (τ) can be calculated using the formula: τ = r * F , heгe r is the radius and F is the force. So, the torque will be 165 N * 1.6m = 264 N.m.
This torque will cause the grindstone to rotate, creating angular acceleration. To calculate the angular acceleration, you need to also know the moment of inertia (I) of the solid disc, which is 0.5*m*r² . Hence I = 0.5 * 75 kg * (1.6m)² = 96 kg.m². Angular acceleration (α) can be calculated by the formula: α = τ / I. Substituting the known values, we get α = 264 N.m / 96 kg.m² = 2.75 rad/sec².
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