A dentist A dentist\'s drill accelerates from rest at 615 rad/s2 for 2.10 s and

Question

A dentist

A dentist's drill accelerates from rest at 615 rad/s2 for 2.10 s and then runs at constant angular velocity for 7.50 s. Through how many total revolutions has the drill turned? This is really two problems, since one part has an acceleration and the other has none. Use the "three equations" for angular motion and select the equation that is useful for the acceleration Then write the appropriate equation (of the three) for the constant angular velocity Then add the two angular displacements (??1+ ??2). Please use these symbols; they are standard for this topic. I want to see an equation written, then vertically substituted into, and finally the result below that, for each stage. It's important to show units in the substitution step

Explanation / Answer

for 2.10 s

theta1 = alpha x t^2 /2 = 615 x 2.10^2 /2 = 1356.08 rad

wf = alphax t = 1291.5 rad/s

theta2 = wf x t = 1291.5 x 7.50 = 9686.25 rad

total theta = theta1+ theta2 = 11042.33

rev = theta / 2 x pi = 1757.44 rev

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