Moment of inertia and rotational motion

Equipment

• Virtual thin hoop and solid disk on a fixed axis
• Sliders “Khối lượng M” (mass) and “Bán kính R” (radius)
• Sliders “Momen lực τ” (torque) and “Tốc độ góc ω” (angular speed)
• Rotatable 3D canvas with angular-acceleration readout

Procedure

1. Set M and R

   Set the mass M and radius R with the two sliders and watch the hoop and disk rotate at the same angular speed. All of the hoop's mass sits at radius R while the disk's mass is spread inward, so $I_{\mathrm{hoop}}=MR^2$ is twice $I_{\mathrm{disk}}=\tfrac12MR^2$; compare the displayed values with these formulas.

2. Apply a torque

   Drag the torque slider τ upward and read the angular acceleration α of each body. The same τ produces a smaller α on the hoop because its I is larger; check that the readout follows $\alpha=\tau/I$.

3. Rotational kinetic energy

   Set an angular speed ω with its slider and compare the rotational kinetic energy stored in each body, $K_{\mathrm{rot}}=\tfrac12I\omega^2$. Then keep M fixed and double R: since $I\propto MR^2$, the stored energy quadruples at the same ω.

4. Predict the spin-up race

   Before touching the sliders, predict which body reaches a target ω first under the same torque, then test it. Repeat with a different M or R and explain each outcome from $I=\int r_\perp^2\,dm$ and $\tau=I\alpha$.

Simulation

Experiment history

Related physicists

Related library topics