What is the tension in the string at the bottom position (magnitude only)?

Question

A 2.2kg object is whirled in a vertical circle whose radius is 1.0m. The object makes 5 complete circles in a time of 4.5s. What is the tension in the string at the bottom position (magnitude only)?

Answer 1

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tension equals centripetal force plus weight

ω = 5 circles/4.5 s x 2π rad/circle = (10/4.5)π rad/s

T = mrω² + mg = (2.2)(1)((10/4.5)π)² + (2.2)(9.8) = 129 NCentripetal force f = mV²/r = mrω²   ω is angular velocity in radians/sec        1 radian/sec = 9.55 rev/min   m is mass in kg   r is radius of circle in meters   V is the tangental velocity in m/s = ωr   f is in Newtons