4. A caveman is swinging a rock on a string in a vertical circle with a radius o

Question

4. A caveman is swinging a rock on a string in a vertical circle with a radius of rotation of 0.4m so that the rock is 0.1m off the ground at the lowest point in its rotation. He wants to hit a fruit in a tree that is 3.2m above the ground. If he releases the rock when it is heading straight up, what is the minimum angular velocity at which he can be swinging the rock? (Hint: you have to know at what height he should release the rock, meaning at what point in its motion is the velocity straight up?) What is the radial (centripetal) acceleration at this speed?

Explanation / Answer

initial height of rock = 0.4+0.1 = 0.5 S = 3.2-0.5 = 2.7 V^2 = U^2 -2gS V = 0 U = 7.27m/sec angular velocity = U/0.4 = 18.18 rad/sec radial acceleration = U^2 / R = 132.277 rad/sec^2

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