Question

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

Answer 1

Initially, it is rotating with an angular velocity of 18 rad/s counter-clock-wise. It has an angular acceleration of 2 rad/s^2 clock-wise, so its counter-clock-wise velocity will slow (and even begin to rotate clock-wise eventually).

Let's call counter-clock-wise motion positive, and clock-wise motion negative.

Then, angular acceleration is constant at -2 rad/s^2.
Initial angular velocity is 18.
And we want to know what time t its angular velocity will be -18.

What do you think we should do next? (Hint: a formula that looks an awful lot like if you were solving for linear velocity.)

Answer 2

ok , then we find that \[\omega (i)=18 , \omega(f)=-18 ,\alpha =-2 \]

when we solve this equation : \[\omega(f)=\omega(i)+\alpha t\]
when we sub the values in Eq : -18=18+(-2)t , so t=18

right ??

Answer 3

That's correct.

Answer 4

Good work.

Answer 5

Okay, thank you so much! I appreciate it! :)

Answer 6

Glad I could help!

Answer 7

Thanks again :)