ACCELERATION (m/s²)
Frictionless Block0.00
Solid Cylinder (I=1/2MR²)0.00
Hollow Cylinder (I=MR²)0.00
Conservation of Energy:
■ Block (Sliding):
No rotation ($I=0$). All potential energy converts entirely into translational kinetic energy.
■ Solid Cylinder (Rolling):
$I = \frac{1}{2}MR^2$. Steals some energy for rotation.
■ Hollow Cylinder (Rolling):
$I = MR^2$. Steals the maximum energy for rotation. Slowest acceleration.
mgh = 1/2 mv² + 1/2 Iω²■ Block (Sliding):
No rotation ($I=0$). All potential energy converts entirely into translational kinetic energy.
a = g*sin(θ)■ Solid Cylinder (Rolling):
$I = \frac{1}{2}MR^2$. Steals some energy for rotation.
a = (g*sin(θ)) / (1 + 1/2) = 2/3 * g*sin(θ)■ Hollow Cylinder (Rolling):
$I = MR^2$. Steals the maximum energy for rotation. Slowest acceleration.
a = (g*sin(θ)) / (1 + 1) = 1/2 * g*sin(θ)