'A push broom consists of a 1.70 metre long handle with mass with mass 0.825kg, with a 0.500m
wide brush with mass 0.420kg attached to the end of the handle'
'Treating both the handle and the brush as thin rods, find the moment of inertia I of the
broom about an axis parallel to the brush and going through the opposite end'
**how is the head of the broom's moment of inertia calculator , is parallel axis theorem used?
To calculate the moment of inertia of the broom's head about an axis parallel to the brush and going through the opposite end, we can use the parallel axis theorem.
The parallel axis theorem states that for an object rotating about an axis parallel to and at a distance 'd' from an axis passing through its center of mass, the moment of inertia about the new axis is given by the sum of the moment of inertia about the center of mass and the product of the mass of the object and the square of the distance 'd'.
In this case, the broom's head consists of the brush attached to the end of the handle. To find the moment of inertia of the broom's head, we need to consider the individual contributions of the handle and the brush and then apply the parallel axis theorem to obtain the total moment of inertia.
The moment of inertia of a thin rod rotating about its center of mass is given by the formula:
I = (1/12) * M * L^2
Where:
I is the moment of inertia
M is the mass of the rod
L is the length of the rod
Applying this formula to the handle, we have:
I(handle) = (1/12) * M(handle) * L(handle)^2
Similarly, the moment of inertia of the brush is calculated using the same formula:
I(brush) = (1/12) * M(brush) * L(brush)^2
Once we have the moment of inertia for each component, we can use the parallel axis theorem to find the total moment of inertia of the broom's head. The distance 'd' in this case would be the length of the handle since the axis is at the opposite end of the handle.
Total moment of inertia of the broom's head:
I(total) = I(handle) + I(brush) + M(brush) * d^2
where M(brush) is the mass of the brush and d is the length of the handle.
After calculating the individual moments of inertia and plugging them into the formula with the appropriate values, you will get the moment of inertia of the broom's head about the chosen axis.