عزم الدوران & Wrench Lab

عزم الدوران & Wrench Lab is an interactive 3D rotational-mechanics simulation that visualizes both the scalar magnitude tau = r F sin theta and the 3D right-hand-rule vector cross product tau = r x F. A steel wrench grips a hexagonal bolt on a workbench while students drag the force grip along the shaft (r from 0.15 m to 0.65 m) and vary the pull angle theta (15 to 165 degrees). Color-coded 3D arrows show the lever arm vector r along the wrench, the applied force vector F, the yellow perpendicular moment arm r_perp = r sin theta, and the vertical green torque vector rising along the bolt axis. Once tau exceeds the breakaway friction threshold, the bolt breaks free and rotates.

• Drag the orange grip handle outward from r = 0.20 m to r = 0.60 m and watch the vertical green عزم الدوران arrow tau = r x F grow until the stuck bolt breaks free and turns.
• محاكاة: Vary Pull angle theta from 30 degrees to 90 degrees and then to 150 degrees, observing how the yellow moment arm r sin theta reaches its maximum when you pull perpendicular to the wrench.
• محاكاة: Click the Snap theta = 90 degrees button or click the hex bolt to align the force perpendicular to the lever arm and compare the torque against an oblique pull.
• محاكاة: Switch to the Top plane (r x F) camera view to inspect the geometric right triangle formed by lever arm r, line of action of F, and perpendicular moment arm r sin theta.
• محاكاة: Increase Bolt breakaway friction to 85 N·m and find the minimum combination of lever arm r and force F needed to loosen the bolt.

1. 1محاكاة: Calculate torque magnitude using tau = r F sin theta and identify the perpendicular moment arm r_perp = r sin theta.
2. 2محاكاة: Use the 3D right-hand rule to determine the axial direction of the torque vector tau = r x F.
3. 3محاكاة: Explain why pulling at 90 degrees to a wrench handle produces maximum torque while pulling along the handle (0 or 180 degrees) produces zero torque.
4. 4محاكاة: Predict whether an applied torque will overcome a static friction threshold and produce angular acceleration.

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