Long description: crank

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A diagram illustrates the connection between a piston undergoing linear motion and a circular wheel undergoing rotational motion via a connecting rod of length l.

Alt text: A diagram shows a connection between a piston and a circular wheel, illustrating the relationship between linear and rotational motion.

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  • The image depicts a mechanical system connecting a straight line (representing a piston's motion) to a circular wheel.
  • On the left, a piston is shown with associated velocity \(\mathbf{v}_p\) and acceleration \(\mathbf{a}_p\) vectors.
  • The piston is connected by a rigid rod of length \(l\) to a point labeled \(C\) on the circumference of a large circle.
  • The circular wheel illustrates rotational motion, with a radius \(r\) drawn from the center to point \(C\).
  • Several vectors are shown on the wheel, indicating linear velocity \(\mathbf{v}_c\) and acceleration \(\mathbf{a}_c\), where the magnitude of the acceleration is given by the equation \(\mathbf{a}_c = \omega^2 r\).
  • The angle \(\theta\) is marked on the circle, indicating the angular position.

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