The instantaneous angular position of a point on a rotating wheel is given by the equation
`theta(t) = 2t^(3) - 6 t^(2)`
The torque on the wheel becomes zero at

Options

A. t=1s
B. `t=0.5 s`
C. `t=0.25 s`
D. `t=2s`

Answer

A

Explanation

`theta(t)=2t^(3)-6t^(2)`
`(d""theta)/(dt)=6t^(2)-12t`
`(d^(2)theta)/(dt^(2))=12t^(2)-12`
Torque, `tau=Ialpha=I((d^(2)theta)/(dt^(2)))=0`
`implies(d^(2)theta)/(dt^(2))=0`
`12t=12`
t=1 second