What is the parallel axis theorem and how is it used? Please explain the equation.
1 answer:
Explanation:
If an object has a moment of inertia I₀ about an axis, then the moment of inertia about a different, parallel axis is I = I₀ + md², where d is the distance between the axes.
For example, consider a horizontal thin rod rotating about a vertical axis passing through its center. It has mass m and length L. Its moment of inertia is known to be I = 1/12 mL².
Now consider the same rod, but this time we move the axis of rotation L/2 to the end of the rod. We can use parallel axis theorem to find the new moment of inertia:
I = I₀ + md²
I = 1/12 mL² + m (L/2)²
I = 1/12 mL² + 1/4 mL²
I = 1/3 mL²
You might be interested in
Answer:
Final velocity is 181.61 m/s at angle 40.44° below horizontal.
Explanation:
Initial horizontal velocity = 170 cos 35.6 = 138.23 m/s
Final horizontal velocity = 138.23 m/s
Considering vertical motion of projectile:
Initial vertical velocity, u = 170 sin 35.6 = 98.96 m/s
Acceleration, a = -9.81 m/s²
Displacement, s = -208 m
We have v² = u² + 2as
Substituting
v² = 98.96² + 2 x -9.81 x -208
v = 117.79 m/s
Final velocity,
Final velocity is 181.61 m/s at angle 40.44° below horizontal.