A wheel rotates around a stationary axis so that the rotation angle θ varies with time as θ$$=kt2$$ , where $$k=1.5$$ rad s−$$2$$ . Find the magnitude of net acceleration of a point P on the rim at the moment $$t=2/3s$$ , if the linear velocity of the point P at this moment is $$v=2$$ ms−$$1$$ .

Question

A  wheel rotates around a stationary axis so that the rotation angle θ      varies with  time as θ$$=kt2$$     , where $$k=1.5$$  rad   s−$$2$$     . Find the magnitude of net acceleration of a point  P on the rim at the moment $$t=2/3s$$     , if the linear velocity of the point P at this  moment is $$v=2$$  ms−$$1$$     .

Infinity Learn · Accepted Answer

ω$$=d$$θ$$dt=ddt(kt2)$$ $$=2kt=2(1.5)t=3t$$ Instantaneous angular acceleration, α$$=d$$ω$$dt=3$$  rad  s−$$2$$ .Note that this is time independent. $$($$ω$$)t=23s=$$α$$t=3(23)=2rad$$  s−$$1$$ $$v=r$$ω ⇒$$r=v$$ω$$=22=1m$$    $$an=v2r=(2)21=4ms$$−$$2$$ And  $$at=r$$α$$=(1)(3)=3$$  ms−$$2$$  $$anet=an2+ar2=42+32=5$$   ms−$$2$$

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A wheel rotates around a stationary axis so that the rotation angle θ varies with time as θ=kt2 , where k=1.5 rad s−2 . Find the magnitude of net acceleration of a point P on the rim at the moment t=2/3s , if the linear velocity of the point P at this moment is v=2 ms−1 .

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