A potter's wheel has the shape of a solid uniform disk of mass $7.0 \mathrm {~kg}$ and radius 0.65 m. It spins about an axis perpendicular to the disk at its center. A small 2.1 kg lump of very dense clay is dropped onto the wheel at a distance 0.41 m from the axis. What is the moment of inertia of the system about the axis of spin? A)1.8 kg ? m² B)1.5 kg ? m² C)0.40 kg ? m² D)2.5 kg ? m²

Question

Quizplus · Accepted Answer

The moment of inertia of the disk is $ I_{\text{disk}} = \frac{1}{2} m r^2 = \frac{1}{2} \times 7.0 \, \text{kg} \times (0.65 \, \text{m})^2 = 1.48 \, \text{kg} \cdot \text{m}^2 $. The moment of inertia of the clay lump is $ I_{\text{clay}} = m r^2 = 2.1 \, \text{kg} \times (0.41 \, \text{m})^2 = 0.35 \, \text{kg} \cdot \text{m}^2 $. The total moment of inertia is $ I_{\text{total}} = I_{\text{disk}} + I_{\text{clay}} = 1.48 + 0.35 = 1.83 \, \text{kg} \cdot \text{m}^2 $, which rounds to 1.8 kg ? m².

A Potter's Wheel Has the Shape of a Solid Uniform 7.0 kg7.0 \mathrm {~kg}7.0 kg

A Potter's Wheel Has the Shape of a Solid Uniform $7.0 \mathrm {~kg}$