Question

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

Answer 1

Correct Answer - a
Given, `theta(t)= 2t^(2)-6t^(2)`
`therefore (d(theta))/(dt) = 6t^(2)-12t, (d^(2)theta)/(dt^(2))=12t-12`
Angular acceleration, `alpha=(d^(2)theta)/(dt^(2))=12t-12`
When angular acceleration `(alpha)` is zero, then the torque on the wheel becomes zero
`rArr 12t-12=0` or t=1s