A potter's wheel has the shape of a solid uniform disk of mass 7.0 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) $2.5 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$
B) $1.5 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$
C) $1.8 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$
D) $0.40 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$

Question

A potter's wheel has the shape of a solid uniform disk of mass 7.0 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) $2.5 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$
B) $1.5 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$
C) $1.8 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$
D) $0.40 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$

Quizplus · Accepted Answer

The moment of inertia of the disk is $ \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 is $ 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 $ 1.48 + 0.35 = 1.83 \, \text{kg} \cdot \text{m}^2 $, which rounds to 1.8.

A Potter's Wheel Has the Shape of a Solid Uniform 2.5 kg⋅m22.5 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }2.5 kg⋅m2

A Potter's Wheel Has the Shape of a Solid Uniform $2.5 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$