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$\bullet$ Electric drill. According to the shop manual, when drilling a 12.7 -mm-diameter hole in wood, plastic, or aluminum, a drill should have a speed of 1250 rev/min. For a 12.7 - -mm-diameter drill bit turning at a constant 1250 $\mathrm{rev} / \mathrm{min}$ , find (a) the maximum linear speed of any part of the bit and (b) the maximum radial acceleration of any part of the bit.

a) $=831.2 \times 10^{-3} \mathrm{m} / \mathrm{s}$b) 108.8 $\mathrm{m} / \mathrm{s}^{2}$

Physics 101 Mechanics

Chapter 9

Rotational Motion

Physics Basics

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

Hope College

Lectures

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In the first part of this question, we have to calculate the maximum velocity, which is represented by v. Let'S begin with the equation to calculate this v v equals to r omega, so call it equation 1. Now, setting the values into this equation, we will get v equals to 12.7, divided by 2 millimeter into 1250 revolutions per minute. Now, converting these values given millimeter into meters and the revolutions per minute into radiant per second. Through some convergence we can write v equals to 12.7 divided by 2 multiplied by 10 rate power, minus 3 meters into 1250, multiplied by 2, pi divided by 60 radiance. So so this will give us v equals to 831.2 multiplied by 10 to power minus 3 meters. Now, let's come toward the second part of this question in this part of the question we have to calculate the radial acceleration, which is a radial in order to calculate this radial. Let me write the equation radial equals to omega square r, so call it equation. 2. Now, setting the values of omega and r, with some convergence, we can write a radial equals to 2250 multiplied by 2 pi divided by 60 radiant per second whole square into 12.7, divided by 2, multiplied by 10, the power minus 3 meters. This will give us a radial equals to 108.8 meter per second square. Thank you.

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