ave speed is half of max ... 1.70 rad/s
stopping time ... 2.50 π rad / 1.70 rad/s
ang acc ... 3.40 rad/s / stopping time
what is the angular acceleration of the wheel
how long does it take for the wheel to come to rest
stopping time ... 2.50 π rad / 1.70 rad/s
ang acc ... 3.40 rad/s / stopping time
2(a)(S)= wf^2 - Wi^2
2 (a)(3.93) = 0^2 - (3.40)^2
7.85a = -11.56
a = -1.472 rad/s/s
So
wf = wi +at
0 = 3.40 - 1.472t
t = 2.3 s
(angular acceleration) = (change in angular velocity) / (change in time)
First, let's find the change in angular velocity. The wheel's initial velocity is given as 3.40 rad/s, and it comes to rest, which means its final velocity is 0 rad/s. So the change in angular velocity is:
(change in angular velocity) = (final angular velocity) - (initial angular velocity)
= 0 rad/s - 3.40 rad/s
= -3.40 rad/s
Next, you need to find the change in time. The wheel rotates 1.25 revolutions before stopping. Since 1 revolution equals 2Ï€ radians, the wheel rotates:
(change in angle) = (1.25 revolutions) * (2Ï€ radians/revolution)
= 2.5Ï€ radians
Now, we can calculate the change in time using the formula:
(change in time) = (change in angle) / (angular velocity)
= (2.5Ï€ radians) / (3.40 rad/s)
≈ 2.32 s
Finally, you can find the angular acceleration by substituting the values into the formula:
(angular acceleration) = (change in angular velocity) / (change in time)
= (-3.40 rad/s) / (2.32 s)
≈ -1.47 rad/s²
Therefore, the angular acceleration of the wheel is approximately -1.47 rad/s². To find how long it takes for the wheel to come to rest, we have already calculated the change in time to be approximately 2.32 seconds.