Block Toppling vs. Sliding & Angular Acceleration Calculator

Block Toppling vs. Sliding & Angular Acceleration Calculator

Determine whether a rectangular block on a wedge will topple before it slides and calculate its initial angular acceleration if it topples.
The critical toppling condition is given by: \[ \tan\phi_{topple} = \frac{L}{H} \] and the sliding threshold is: \[ \tan\phi_{slide} = \mu. \] The block will topple if \(\mu > \frac{L}{H}\).
If toppling occurs, the angular acceleration is: \[ \alpha = \frac{3g\,(L\cos\phi – H\sin\phi)}{2\,(L^2+H^2)}. \]

* Enter the wedge angle (φ in °), coefficient of friction (μ), block base length (L) and height (H) in meters, and gravitational acceleration (g in m/s²).

Step 1: Enter Parameters

Example: 25°

Example: 0.6

Example: 0.4 m

Example: 0.8 m

Example: 9.81 m/s²

Critical Toppling Angle: \( \phi_{topple} = \arctan\left(\frac{L}{H}\right) \)
Sliding Threshold Angle: \( \phi_{slide} = \arctan(\mu) \)

Angular Acceleration (if toppling): \( \alpha = \frac{3g\,(L\cos\phi – H\sin\phi)}{2\,(L^2+H^2)} \) rad/s²


Practical Example:
For a wedge angle of 25°, \(\mu = 0.6\), \(L = 0.4\) m, \(H = 0.8\) m, and \(g = 9.81\) m/s²:
– Critical Toppling Angle: \( \phi_{topple} \approx \arctan(0.4/0.8) \approx 26.57° \)
– Sliding Threshold Angle: \( \phi_{slide} \approx \arctan(0.6) \approx 30.96° \)
Since \(26.57° < 30.96°\), the block topples before sliding.
The initial angular acceleration is then given by the above formula.