A wagon wheel consists of 8 spokes of uniform diameter, each of mass ms and length L cm. The outer ring has a mass mring. What i
1 answer:
Answer:
The moment of inertial of the wheel,
Explanation:
Given;
8 spokes of uniform diameter
mass of each spoke, =
length of each spoke, = L
mass of outer ring, =
The moment of inertial of the wheel will be calculated as;
where;
is the moment of inertia of each spoke
is the moment of inertia of the rim
Moment of inertia of each spoke
Moment of inertial of the wheel
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Answer:
46.2 rad/s2
Explanation:
Angular acceleration works very similar to linear acceleration, it follows this equation:
Where:
γ: angular acceleration
Mt: torque
J: moment of inertia of the load from its turning axis
Since we have the torque we just need the moment of inertia. We have to add together the moments of the drive shaft, tires, wheel walls and wheels.
The wheels act like disks. For disks the moment of inertia is:
The wheel walls act like annular rings, for these the moment of inertia is:
The tread acts like a hoop, as in mass concentrated into a circunference, for these:
The axle acts like a rod, which is the same as the disk:
The drive shaft acts like a rod too:
SO, the total moment of inertia is:
J = 2*Jwheel + 2*Jwall + 2*Jtread + Jaxle + Jshaft
J = 2*0.243 + 2*0.07 + 2*1.09 + 0.0028 + 0.016 = 2.82 kg*m2
Finally the angular acceleration is: