The instantaneous angular position of a point on a rotating wheel is given by the equation $Q(t)=2 t^3-6…

The instantaneous angular position of a point on a rotating wheel is given by the equation $Q(t)=2 t^3-6 t^2$ The torque on the wheel becomes zero at
  1. $t=0.5 \mathrm{~s}$
  2. $t=0.25 \mathrm{~s}$
  3. $t=2 \mathrm{~s}$
  4. $t=1 \mathrm{~s}$

Solution

According to question, torque, $\tau=0$ Its means that, $\alpha=0$ $\alpha=\frac{d^2 \theta}{d t^2}$ Given So $\theta(t)=2 t^3-6 t^2$ $\begin{aligned} \frac{d \theta}{d t} & =6 t^2-12 t \\ \frac{d^2 \theta}{d t^2} & =12 t-12 \quad\left(\because \alpha=\frac{d^2 \theta}{d t^2}=0\right) \\ 12 t-12 & =0 \\ t & =1 \mathrm{~s} \end{aligned}$

Asked in: NEET 2011 (Screening)

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