A drill bit is driven by an electric motor about a fixed axis

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A drill bit is driven by an electric motor about a fixed axis. The motion of the bit proceeds through three consecutive stages: Stage I: From t=0t = 0 to t=2.0 st = 2.0\,\text{s}, the bit starts from rest and speeds up with a uniform angular acceleration until it reaches ω1=1200 rev min−1\omega_1 = 1200\,\text{rev}\,\text{min}^{-1}. Stage II: From t=2.0 st = 2.0\,\text{s} to t=3.5 st = 3.5\,\text{s}, the bit slows down uniformly to ω2=800 rev min−1\omega_2 = 800\,\text{rev}\,\text{min}^{-1}. Stage III: From t=3.5 st = 3.5\,\text{s} to t=6.5 st = 6.5\,\text{s}, the bit maintains the constant angular velocity ω2\omega_2. (Use 1 rev=2π rad1\,\text{rev} = 2\pi\,\text{rad}.) (a) Convert ω1\omega_1 and ω2\omega_2 to SI units of rad s−1\text{rad}\,\text{s}^{-1}. (b) Determine the angular acceleration during Stage I and during Stage II. State the sign of each value. (c) Calculate the angular displacement of the bit during each stage, then compute the total angular displacement for the entire 6.5 s6.5\,\text{s} interval. (d) Compute the average angular velocity and the average angular acceleration for the bit over the whole 6.5 s6.5\,\text{s} period. (e) Explain why the average angular acceleration for the entire motion is not simply the average of the accelerations found for Stages I and II.

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