A bicycle is turned upside down while its owner repairs a flat tire. A friend sp

Question

A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel and observes that drops of water fly off tangentially. She measures the heights reached by drops moving vertically (see figure). A drop that breaks loose from the tire on one turn rises vertically 54.0 cm above the tangent point. A drop that breaks loose on the next turn rises 51.0 cm above the tangent point. The radius of the wheel is 0.323 m.

(a) Why does the first drop rise higher than the second drop? This answer has not been graded yet.

(b) Neglecting air friction and using only the observed heights and the radius of the wheel, find the wheel's angular acceleration (assuming it to be constant).

Explanation / Answer

(a) Because the initial tangential velocity with which the drop rises decreases every turn, i.e. the wheel is decelerating.

(b) Initial tangential velocity in first turn, v1 = (2gh1)1/2

Initial tangential velocity in next turn, v2 = (2gh2)1/2

Angular acceleration = (v2 - v1) / r2 = (2g)1/2[h21/2 - h11/2] / r2 = (2 * 9.8)1/2[0.511/2 - 0.541/2] / 0.3231/2 = -0.88 m/s2

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