Question #125876

5. At a given time a shaft is rotating 50 rpm about a fixed axis, 20 s later it is rotating 1050 rpm. Solve its angular acceleration.

Expert's answer

By definition, the angular acceleration is:

where "\\Delta \\omega" is angular velocity change during the time "\\Delta t".

The "\\Delta \\omega" can be calculated as following (as far as one revolution corresponds to "2\\pi" radians):

"\\Delta \\omega = (1050rpm - 50rpm)\\cdot 2\\pi = 2000\\pi \\space rad\/m \\approx 104.7\\space rad\/s"

Thus, the angular acceleration will be:

**Answer. **5.2 rad/s^2.

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