Related rates: Piston and flywheel. The piston shown is driving the flywheel. When the crank is in the position shown, the design requires that the flywheel have a speed of 0.4 radians/sec. Find the corresponding speed of the piston. Further data is that the acute angle shown is 30 degrees , and the radius of the crank is 15 cm.

Since the piston is constrained to move only in the x direction, we need the speed of the projection of the crank joint onto the x-axis:

.

We can differentiate this expression to find the relationship between the speed of the piston and the angular speed of the flywheel:

, where the minus sign indicates that the piston is moving to the left.

Now we can substitute the given data to find