First slide

Dynamics of rotational motion about fixed axis

Question

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

Moderate

A

t = 0.5 s
B

t = 0.25 s
C

t = 2s
D

t = 1 s

Solution

The instantaneous angular position of a point on a rotating wheel is given by the equation $θ (t) = 2 t^{3} - 6 t^{2}$
According to question, torque, $τ = 0$
its means that, $α = 0$
$α = \frac{d^{2} θ}{{dt}^{2}}$
Given $θ (t) = 2 t^{3} - 6 t^{2}$
So, $\frac{dθ}{dt} = 6 t^{2} - 12 t$
$\frac{d^{2} θ}{{dt}^{2}} = 12 t - 12 (α = \frac{d^{2} θ}{{dt}^{2}} = 0)$
12t-12 = 0
t = 1 s

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