Estimate the moment of inertia of a bicycle wheel 67 cm in diameter. The rim of the tire have a combination mass of 1.1kg.
(1.1)(67) = 73.3
To estimate the moment of inertia of a bicycle wheel, you can assume it behaves like a thin hoop with all the mass concentrated in the rim. The moment of inertia of a thin hoop can be calculated using the formula:
I = M * R^2
Where:
I is the moment of inertia
M is the mass of the rim
R is the radius of the wheel (half the diameter)
In this case, the diameter of the wheel is given as 67 cm, so the radius (R) would be half of 67 cm, which is 33.5 cm (or 0.335 m).
The mass of the rim (M) is given as 1.1 kg.
Now, let's substitute the values into the formula:
I = M * R^2
I = (1.1 kg) * (0.335 m)^2
I = 1.1 kg * 0.112225 m^2
I ≈ 0.123 ms^2
Therefore, the estimated moment of inertia of the bicycle wheel is approximately 0.123 kg m^2.