Question

A crank on an engine has rotating parts of mass 4.25kg, with a radius of gyration k = 59 mm. Determine the torque in Nm required to overcome the inertia of the rotating parts when angular acceleration is 36 rads/s2

Answer 1

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Answer on Question #44568, Physics, Mechanics | Kinematics | Dynamics

Question:

A crank on an engine has rotating parts of mass $4.25\mathrm{kg}$, with a radius of gyration $k = 59$ mm. Determine the torque in Nm required to overcome the inertia of the rotating parts when angular acceleration is 36 rads/s²

Answer:

Newton's second law of motion adapted to describe the relation between torque and angular acceleration:

$$\tau = I \alpha$$

where $\tau$ – torque, $I$ – moment of inertia, $\alpha$ – angular acceleration.

Moment of inertia equals:

$$I = m k^2$$

where $m$ is mass, $k$ is radius of gyration.

Therefore:

$$\tau = \alpha m k^2 = 36 \cdot 4.25 \cdot 0.059^2 \cong 0.533 \, N \cdot m$$

Answer: $0.533 \, N \cdot m$