All Problems

Kinematics

Problem 1.44

A wheel rotates around a stationary axis so that the rotation angle \(\varphi\) varies with time as \(\varphi=a t^{2},\) where \(a=0.20 \mathrm{rad} / \mathrm{s}^{2} .\) Find the total acceleration \(w\) of the point \(A\) at the rim at the moment \(t=2.5 \mathrm{~s}\) if the linear velocity of the point \(A\) at this moment \(v=0.65 \mathrm{~m} / \mathrm{s}\).

Reveal Answer
w=(v/t)1+4a2t4=0.7 m/s2w=(v / t) \sqrt{1+4 a^{2} t^{4}}=0.7 \mathrm{~m} / \mathrm{s}^{2}
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