# A piston is connected by a rod of #14 cm# to a crankshaft at a point #5 cm# away from the axis of rotation. Determine how fast the crankshaft is rotating when the piston is 11 cm away from the axis of rotation and is moving toward it at 1200 cm/s?

So we know that:

Before we start, let's write out a formula for theta given what we know, using the Law of Cosines:

Now, take the derivative of this with respect to time:

Or if you prefer decimal form:

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To determine the angular velocity of the crankshaft, use the formula: ω = v / r, where ω is the angular velocity, v is the velocity of the piston, and r is the distance from the piston to the axis of rotation. Given v = 1200 cm/s and r = 11 cm, plug in the values to find ω.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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