A T is made of two identical 740 g thin solid rods. The moment of inertia of the T about an axis perpendicular to the screen through point at one end of a rod is determined experimentally to be 0.68 kg-m2. What is the length of the rods?
I have no idea where the screen is. But I suspect you need the parallel axis theorem.
The answer depends upon which end of which rod is the axis of rotation. You have not provided that information. Is it there the rods intersect? Or the bottom of the "T" ?
the bottom of the T
To find the length of the rods, we can use the formula for the moment of inertia of a thin rod rotating about its end.
The moment of inertia of a thin rod rotating about one end is given by the formula:
I = (1/3) * m * L^2
Where:
- I is the moment of inertia
- m is the mass of the rod
- L is the length of the rod
In this case, we have two identical rods, so we can write the equation as:
2 * (1/3) * m * L^2 = 0.68 kg-m^2
Now, we need to solve for L, the length of the rods.
First, we simplify the equation:
(2/3) * m * L^2 = 0.68 kg-m^2
Next, we substitute the mass value given:
(2/3) * 0.74 kg * L^2 = 0.68 kg-m^2
Now, we can solve for L by rearranging the equation:
L^2 = (0.68 kg-m^2) / [(2/3) * 0.74 kg]
L^2 = 0.68 kg-m^2 * (3/2) / 0.74 kg
L^2 = 1.62 m^2
Taking the square root of both sides, we get:
L ≈ 1.27 m
Therefore, the length of each rod is approximately 1.27 meters.