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The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity ω, as shown. Assume the length of the crank to be r. Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where the crank is parallel to x-axis, is given by

1. −ω²r
2. 2ω²r
3. ω²r
4. −2ω²r

Correct answer: −ω²r

Solution

The acceleration of the slider in the y-direction is determined by the centripetal acceleration due to the rotation of the crank. When the crank is parallel to the x-axis, the vertical component of the acceleration is negative, resulting in an expression of -ω²r, which reflects the downward acceleration of the slider.

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