Question

A wheel initially has an angular velocity of $18rad/s$.IT has a constant acceleration of $2.0rad/s^2$ and is slowing at first.What time elapses before its angular velocity is $18rad/s$ in the direction opposite to its initial angular velocity?

• A. $3.0s$
• B. $6.0s$
• C. $9.0s$
• D. $18s$

Answer 1

The correct option is D $18s$

Given initial angular velocity ${\omega }_i=18$ rad/s

final angular velocity ${\omega }_f=-18$ rad/s

And we know acceleration $\alpha =\frac{{\omega }_f-{\omega }_i}{t}=\frac{-18-18}{t}$

$t=\frac{-36}{2}=-18=18$ s