A wheel starting from rest is uniformely accelerated at `2 rad//s^(2)` for `5 s`. It is allowed to rotated uniformly for the next `10 s` and is finally brought to rest in the next `5 s`. Find the total angle rotated by the wheel.

Explanation

`t=0` to `t=5 s` (uniform angular acceleration)
` theta_(1)=omega_(0) t+(1)/(2)alpha t^(2)`
` = 0+(1)/(2)xx2xx5^(2)= 25rad`
`omega_(1)=omega_(0)+alpha t=0+2xx5=10 rad//s`
`t=5` to `t=15 s` (uniform angular velocity)
` theta_(2)=omega_(1)(15-5)=10(10)=100 rad`
`t=15` to `t=20 s` (uniform angular retardation)
` theta_(3)=omega_(1) t-(1)/(2)alpha t^(2)`
` = 10xx5-(1)/(2)xx2xx5^(2)=25 rad`
Total angle `=theta_(1)+theta_(2)+theta_(3) = 25+100+25= 150 rad `
OR

The area of `omega-t` will give angular displacement
`theta=(1)/(2)(10+20)xx10`
`=150 rad`