Posted by sandhu on Tuesday, November 30, 2010 at 7:38pm.
Posted by sandhu on Tuesday, November 30, 2010 at 1:17am.
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?
physics - bobpursley, Tuesday, November 30, 2010 at 9:33am
I have no idea where the screen is. But I suspect you need the parallel axis theorem.
physics - drwls, Tuesday, November 30, 2010 at 9:41am
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" ?
physics - sandhu, Tuesday, November 30, 2010 at 7:27pm
the bottom of the T or at the top of an inverted T
To solve this problem, you need to use the parallel axis theorem, which relates the moment of inertia of an object about an axis to its moment of inertia about a parallel axis that is a distance away from the original axis.
In this case, the moment of inertia of the T about an axis perpendicular to the screen through a point at one end of a rod is given as 0.68 kg-m^2.
However, the length of the rods is not provided, and we need that information to solve the problem.
To find the length of the rods, we can use the parallel axis theorem.
The parallel axis theorem states that the moment of inertia about an axis parallel to and a distance "d" away from an axis through the center of mass is related to the moment of inertia about the center of mass axis by the equation:
I = I_cm + Md^2
Where:
I is the moment of inertia about the axis perpendicular to the screen through a point at one end of the rod (given as 0.68 kg-m^2).
I_cm is the moment of inertia about the center of mass axis.
M is the mass of the rod (given as 740 g, which is 0.74 kg).
d is the distance between the axis through the center of mass and the axis perpendicular to the screen.
To find the length of the rods, we can rearrange the equation and solve for d:
d = sqrt((I - I_cm) / M)
Substituting the given values:
d = sqrt((0.68 kg-m^2 - I_cm) / 0.74 kg)
However, the moment of inertia about the center of mass axis (I_cm) is not given in the problem statement. Therefore, we cannot solve for the length of the rods without this information.