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At t=0 a grinding wheel has an angular velocity of 20.0 rad/s . it has a constant angular acceleration of 35.0 rad/s2 until a circuit breaker trips at time t = 2.30 s . from then on, it turns through an angle 433 rad as it coasts to a stop at constant angular acceleration. part a through what total angle did the wheel turn between t=0 and the time it stopped?

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LammettHash

Over the first 2.30 s, the wheel turns by angle [tex]\theta[/tex] according to

[tex]\theta=\left(20.0\dfrac{\rm rad}{\rm s}\right)t+\dfrac12\left(35.0\dfrac{\rm rad}{\mathrm s^2}\right)t^2[/tex]

so that after 2.30 s, it will have turned

[tex]\theta=138.575\,\mathrm{rad}[/tex]

Then the wheel turns a total of [tex]\theta+433\,\mathrm{rad}[/tex] over this entire interval, or [tex]572\,\mathrm{rad}[/tex].

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