The moment of inertia of a 0.98 kg bicycle wheel rotating about its center is 0.13 km-m^2. What is the radius of the wheel? Ignore the mass of the wheel's spokes.
To find the radius of the bicycle wheel, we can use the formula for the moment of inertia of a solid cylinder rotating about its center:
I = (1/2) * m * r^2
Here, I is the moment of inertia, m is the mass of the wheel, and r is the radius of the wheel.
Given that the moment of inertia I is 0.13 km-m^2 (convert it to m^2 by multiplying by 1000*1000), and the mass m is 0.98 kg, we can plug these values into the formula and solve for r.
0.13 km-m^2 = (1/2) * 0.98 kg * r^2
To simplify the equation and solve for r, we can rearrange the equation as follows:
r^2 = (2 * 0.13 km-m^2) / 0.98 kg
r^2 = 0.266122 km-m^2/kg
Now, we need to convert the right side of the equation to meters:
r^2 = 0.266122 * 1000 m^2/kg
r^2 = 266.122 m^2/kg
Finally, take the square root of both sides to find the radius:
r = √(266.122 m^2/kg)
r ≈ 16.314 m
Therefore, the radius of the bicycle wheel is approximately 16.314 meters.