Final answer:
The mass of the cylindrical disk mounted on an axle that acquires an angular acceleration of 120 rad/s^2 when a tangential force of 45 N is applied is 6.25 kg.
Step-by-step explanation:
To determine the mass of the cylindrical disk, we can use Newton's second law for rotation, which states that the torque (τ) applied to an object is equal to its moment of inertia (I) multiplied by its angular acceleration (α), given by the equation τ = Iα.
The torque can also be calculated by the product of the force applied (F) and the radius (r) of the disk provided the force is applied tangentially, τ = rF. In this case, we have a force (F) of 45 N applied at a radius (r) of 0.15 m which gives us a torque.
Using the formula for torque:
τ = rF = (0.15 m)(45 N) = 6.75 Nm
Since the moment of inertia (I) of a solid cylinder about its center is given by I = (1/2)m²r, we can re-arrange Newton's second law for rotation to solve for the mass (m), m = 2τ / (r2α).
Substituting our known values in:
m = 2 * 6.75 Nm / (0.15 m)2 * 120 rad/s2
m = 13.50 / 0.018 * 120
m = 13.50 / 2.16
Therefore, the mass of the disk is 6.25 kg.