Chapter 8: Problem 47
Verify that the units of the rotational form of Newton's second law [Eq. (8-9)] are consistent. In other words, show that the product of a rotational inertia expressed in \(\mathrm{kg} \cdot \mathrm{m}^{2}\) and an angular acceleration expressed in \(\mathrm{rad} / \mathrm{s}^{2}\) is a torque expressed in \(\mathrm{N} \cdot \mathrm{m}\).
Short Answer
Expert verified
Answer: Yes, the units of the rotational form of Newton's second law are consistent. The product of rotational inertia (\(\mathrm{kg} \cdot \mathrm{m}^{2}\)) and angular acceleration (\(\mathrm{rad}/\mathrm{s}^{2}\)) results in the same units as torque (\(\mathrm{N}\cdot\mathrm{m}\)), which confirms the consistency.