Trebuchet
A simplified rigid-beam trebuchet: counterweight and projectile lie on one line through the pivot. Gravity creates a torque τ = g cos θ (M r_cw − m r_p); angular acceleration follows τ/I. When the beam reaches the release angle, the projectile detaches with tangential speed v = r_p ω and moves as a free projectile.
Who it's for: Mechanics courses covering torque, rotation, and energy transfer; medieval siege-engine demos.
Key terms
- torque
- moment of inertia
- angular acceleration
- tangential velocity
- range
- lever arm
How it works
A rigid beam pivots on a fixed axle: a heavy counterweight on the short arm and the projectile on the long arm. Gravity produces a torque that accelerates rotation; when the beam reaches the release angle, the projectile leaves with tangential speed v = rω and follows a parabola. Adjust masses, arm lengths, start angle, and release angle to maximize range.
Key equations
τ = g cos θ (M r_cw − m r_p), I = M r_cw² + m r_p² + I_beam, α = τ / I
At release: v = r_p ω (−sin θ, cos θ); then ẍ = 0, ÿ = −g
Frequently asked questions
- Why does a heavier counterweight or longer projectile arm increase range?
- A larger M r_cw − m r_p gives more torque early in the swing, so ω at release is higher. A longer r_p also increases launch speed v = r_p ω, which strongly increases range.
- What is missing compared to a real trebuchet?
- Real machines have a sling, sliding axle, beam mass distribution, friction, and aerodynamic drag. This model keeps a rigid beam and instant release for clarity.
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