A wagon wheel consists of 8 spokes of uniform diameter,each of mass m_s and length L cm.The outer ring has a mass m_ring.What is the moment of inertia of the wheel? Assume that each spoke extends from the center to the other ring and the ring is of negligible thickness.

Question

Quizplus · Accepted Answer

The moment of inertia of the wagon wheel can be found by considering the moment of inertia of each spoke, as well as the moment of inertia of the outer ring.

The moment of inertia of each spoke is given by: 
Ispoke = (1/12) m L^2

Since there are 8 spokes, the total moment of inertia due to the spokes is: 
Ispokes = 8(1/12) m L^2 = (2/3) m L^2

The moment of inertia of the outer ring is given by: 
Iring = (1/2) mR^2

Since the ring is thin, its radius is equal to the radius of the wheel. The radius of the wheel is L/2, so 
Iring = (1/2) m(L/2)^2 = (1/8) m L^2

Therefore, the total moment of inertia of the wagon wheel is: 
I = Ispokes + Iring = (2/3) m L^2 + (1/8) m L^2 = (17/24) m L^2

The correct answer choice is B.

A Wagon Wheel Consists of 8 Spokes of Uniform Diameter,each