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- Summary
- My theory/computer program gives a bigger result than my experiment. I may have the "moment of inertia" wrong.

I am interested in climate change and thereby interested in tipping points. So for the last few months, I have been investigating the dynamics of a toppling brick. I derived a differential equation of for the motion and wrote a computer program to solve this from initial conditions.

I have more detail and a diagram on

https://www.feedbackreigns.net/tipping-points/

Trouble is that my computer output suggests a longer toppling time than my experiment with a brick.

I suspect my moment of inertia may be wrong.

Inertia = M * (W * W + H * H) / 12 + M * R * R

I did a primitive experiment. I used some cut cardboard to give my red brick an initial tilt of 35 degrees from the vertical. Then I let it rotate from rest to the ground (tilt = 90 degrees), recording the sound of this on a mobile phone. It all happens so fast.

The experimental toppling time is about 0.4 or 0.5 seconds.

My calculation is out by about a factor of 6.

My program gives a much larger result.

Block Mass: kilogram = 4.06

Block Height: metre = 0.225

Block Width: metre = 0.104

Brick Depth = 0.075 is not used in my calculations

Initial Tilt from vertical: degrees = 35.0

Initial tilt speed: degrees/sec = 0.0

Radius of motion of Centre of mass: metre = 0.12394

Tipping point Angle: degrees = 24.80745

Initial Tilt past tipping point: degrees = 10.19255

Acceleration of gravity = 9.8

Moment of inertia: kg metre^2 = 0.08315

Acceleration factor = 59.30457

Maximum Tilt: degrees 90.00010

Topple Time: seconds = 2.52319

TiltStep for numerical calculation = 1 degree

Can anyone suggest why I get this discrepancy between theory and experiment?

I have more detail and a diagram on

https://www.feedbackreigns.net/tipping-points/

Trouble is that my computer output suggests a longer toppling time than my experiment with a brick.

I suspect my moment of inertia may be wrong.

Inertia = M * (W * W + H * H) / 12 + M * R * R

I did a primitive experiment. I used some cut cardboard to give my red brick an initial tilt of 35 degrees from the vertical. Then I let it rotate from rest to the ground (tilt = 90 degrees), recording the sound of this on a mobile phone. It all happens so fast.

The experimental toppling time is about 0.4 or 0.5 seconds.

My calculation is out by about a factor of 6.

My program gives a much larger result.

Block Mass: kilogram = 4.06

Block Height: metre = 0.225

Block Width: metre = 0.104

Brick Depth = 0.075 is not used in my calculations

Initial Tilt from vertical: degrees = 35.0

Initial tilt speed: degrees/sec = 0.0

Radius of motion of Centre of mass: metre = 0.12394

Tipping point Angle: degrees = 24.80745

Initial Tilt past tipping point: degrees = 10.19255

Acceleration of gravity = 9.8

Moment of inertia: kg metre^2 = 0.08315

Acceleration factor = 59.30457

Maximum Tilt: degrees 90.00010

Topple Time: seconds = 2.52319

TiltStep for numerical calculation = 1 degree

Can anyone suggest why I get this discrepancy between theory and experiment?

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