Question

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?

Answer 1

Over the first 2.30 s, the wheel turns by angle
`\theta` according to

`\theta=\left(20.0(\rm rad)/(\rm s)\right)t+\frac12\left(35.0(\rm rad)/(\mathrm s^2)\right)t^2`

so that after 2.30 s, it will have turned

`\theta=138.575\,\mathrm{rad}`

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