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 $I_{\text{disk}} = \frac{1}{2} m r^2 = \frac{1}{2} \times 7.0 \times (0.65)^2 = 1.48 \, \text{kg} \cdot \text{m}^2$. The moment of inertia of the clay is $I_{\text{clay}} = m r^2 = 2.1 \times (0.41)^2 = 0.35 \, \text{kg} \cdot \text{m}^2$. 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 $7.0 \mathrm {~kg}$