A wheel has an initial velocity of 3.40rad/s and it rotates 1.25 revolutions before stopping
what is the angular acceleration of the wheel
how long does it take for the wheel to come to rest
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
1.25 revolutions = 3.93 radians
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
To find the angular acceleration of the wheel, you'll need to use the following formula:
(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 2π radians, the wheel rotates:
(change in angle) = (1.25 revolutions) * (2π radians/revolution)
= 2.5π radians
Now, we can calculate the change in time using the formula:
(change in time) = (change in angle) / (angular velocity)
= (2.5π 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.