Double Cone Rolling Uphill

The cone rolls up the track, but its center of mass moves downward

Controls

Rolling Object

Cone

Track Opening Angle α

α = 25°

Cone Side Angle β

β = 18°

Track Upward Angle γ

γ = 5.0°

Cone Base Radius R

R = 0.80 m

Friction / Energy Loss

loss = 0.03

θ = geometry angle showing how much the cone’s center of mass tends to move downward
θ = 6.4°
Condition: γ < θ
Effective slope: 1.4°
x = 0.00 m
r = 0.80 m
v = 0.00 m/s

Home

Energy Distribution
KE: 0.00 J
PE lost: 0.00 J
Thermal: 0.00 J

PE Lost

Thermal

The center of mass goes down even though the cone appears to roll up.

Graphs

Center of Mass Height vs Position

Speed vs Position

Rolling Radius vs Position

Double Cone Rolling Uphill Physics Simulation

This interactive 3D physics simulation demonstrates the famous double cone rolling uphill or defying gravity illusion. The double cone appears to roll upward along a V-shaped track, but the actual center of mass moves downward.

Why Does the Double Cone Roll Uphill?

The V-shaped track becomes wider as the cone moves forward. Because the cone is thicker near the middle and narrower near the ends, the support points move outward and the center of mass can become lower even while the rails themselves rise.

sin θ = tan α tan β

Here, α represents the opening angle of the V-shaped track, and β represents the cone angle. The angle θ describes the effective downward direction of the center of mass when the track is flat.

Condition for Rolling Against the Slope

If the track is tilted upward by angle γ, the cone will still roll in the direction that looks uphill when:

γ < θ

In this case, the rails rise, but the center of mass decreases in height. Gravity is not violated. The motion is still caused by gravitational potential energy decreasing.

Energy Conservation and Rolling Without Slipping

The rolling condition connects translational and rotational motion:

v = rω

The effective rolling radius changes as the cone moves along the track:

r = R - x tan θ

As the radius becomes smaller, the cone can spin faster even if the forward speed eventually slows down. This makes the double-cone motion different from a simple cylinder rolling down a ramp.

What Students Learn

The apparent motion of an object can be different from the motion of its center of mass.
Gravity lowers the center of mass; it does not pull the cone uphill.
The V-shaped track geometry controls whether the illusion works.
Rolling without slipping connects linear speed, angular speed, and effective radius.
Energy conservation explains the motion without violating gravity.

How to Use This Simulation

Increase α to make the V-shaped track open faster.
Increase β to change the cone geometry.
Increase γ to make the physical track slope upward more steeply.
Watch the condition γ < θ. If γ becomes too large, the cone cannot roll “uphill.”
Observe the yellow center-of-mass marker and the graphs to see that the center of mass moves downward.