Calculate the moment of Inertia for a ring with a mass 0.715 kg, an inner radius of 10.7 cm and an outer radius of 12.7 cm.
m•(R² + r ²)/2
I=0.5*M*(R^2+r^2)
I=0.5*0.715kg*[(12.7cm)^2+(10.7cm)^2]
I=98.6 kg*cm^2
Oh, I love a good physics problem! Let's calculate the moment of inertia for this ring.
First, we need to remember the formula for the moment of inertia of a ring:
I = (m * (r_outer^2 + r_inner^2)) / 2
where I is the moment of inertia, m is the mass, r_outer is the outer radius, and r_inner is the inner radius.
Plugging in the values we have:
I = (0.715 kg * ((0.127 m)^2 + (0.107 m)^2)) / 2
Calculating that out, we get:
I ≈ 0.019 kg·m²
So, the moment of inertia for this ring is approximately 0.019 kg·m². Just remember to keep that number safe because the moment of inertia can be quite moody without proper supervision.
To calculate the moment of inertia for a ring, we can use the formula:
I = (m * (r_outer^2 + r_inner^2)) / 2
Where:
- I is the moment of inertia
- m is the mass of the ring
- r_outer is the outer radius of the ring
- r_inner is the inner radius of the ring
Let's plug in the values:
m = 0.715 kg
r_outer = 12.7 cm = 0.127 m
r_inner = 10.7 cm = 0.107 m
I = (0.715 * (0.127^2 + 0.107^2)) / 2
Now we can solve this equation to find the moment of inertia.
To calculate the moment of inertia of a ring, we can use the formula:
I = (m * (r_outer^2 - r_inner^2)) / 2
where:
I = moment of inertia
m = mass of the ring
r_outer = outer radius of the ring
r_inner = inner radius of the ring
Let's plug in the given values:
m = 0.715 kg
r_outer = 12.7 cm = 0.127 m
r_inner = 10.7 cm = 0.107 m
Now we can substitute these values into the formula:
I = (0.715 kg * (0.127 m)^2 - (0.107 m)^2) / 2
Calculating the values inside the parentheses:
I = (0.715 kg * (0.016129 m^2) - (0.011449 m^2)) / 2
I = (0.011588 m^2 - 0.000131 m^2) / 2
I = 0.011457 m^2 / 2
Finally, calculating the moment of inertia:
I = 0.0057285 kg * m^2
Therefore, the moment of inertia for the given ring is approximately 0.0057285 kg * m^2.