Question

A yo-yo can be modelled as a cylinder with radius r and mass m (I = ½mr2). While hanging at the bottom of a string, the yo-yo is given initial upward velocity and initial rotational velocity, and as it moves upward the string is wrapped around the cylinder (for simplicity, assume the string wraps around the full radius). Determine the tension in the string as the yo-yo moves upward.

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Answer 1

Here we apply Newton's laws of motion and rotation.

AM AT To fa | Angular acceleration = a Linear acceleration = a Luputard): As no slipping of string on yo-yo. o a=ar Apply Motion Newton's law of - temg ma ST = mo tal Newton's law of rotation Torque about center of yoyo. - Tret = (ID ) » Ia = Toro - Imr 2a = Tor) T == ma as a=ar - Ima = m (9 ta) -qgua → a= -29 T = -1 2m (28) 3 &