Moment of inertia: masses on a bar

Drag either metal block. Both move symmetrically about the midpoint.

Move the masses or the axis

Axis perpendicular to the page

Bar: 1 kg, length 4 m. Each block: 1 kg. Distances are measured to the blocks' centers.

Moment of inertia about this axis

kg m²

Bar
Left block
Right block

Inertia as the masses move

Curve: current axis position. Dot: current mass positions.

Each mass from midpoint, d m

Axis position, a m

Snap to 0.25 m gridShow calculation

Tab to a mass or the axis and use Left/Right to move. R reset · H controls · T theme · F11 full screen.

The bar and the metal blocks

The two equal blocks slide along the bar. Their centers stay at -d and +d, measured from the bar's midpoint, so the center of mass of the whole system stays at the midpoint. The axis is perpendicular to the page and can move along the bar.

Object	Mass	Dimensions in the page
Uniform bar	1 kg	4 m by 0.10 m
Each uniform block	1 kg	0.50 m by 0.30 m

The masses can move from d = 1.75 m, with their outer edges at the bar's ends, to d = 0.25 m, where they meet at the midpoint. They do not overlap.

Finite block size and the bar's own inertia are included. For a uniform rectangle of mass m, width w and height h, about an axis perpendicular to the rectangle:

I_{CM} = \frac{m}{12} (w^{2} + h^{2}), I = I_{CM} + m r^{2}

Each distance r runs from the axis to that object's center of mass.