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The wheel on a vehicle has a rotational inertia of 2.0 kg*m^2. at the instant the wheel has a counterclockwise angular velocity of 6.0 rad/s, an average counterclockwise torque of 5.0 n*m is applied, and continues for 4.0 s. what is the change in angular momentum of the wheel?

Respuesta :

skyluke89
We can use the equivalent of 
[tex]F= \frac{\Delta p}{\Delta t} [/tex]
for rotational motions:
[tex]\tau= \frac{\Delta L}{\Delta t} [/tex]
where
[tex]\tau[/tex] is the torque applied to the object
[tex]\Delta L[/tex] is the variation of angular momentum
[tex]\Delta t[/tex] is the time interval

In our problem, [tex]\tau=5.0 Nm[/tex] and [tex]\Delta t=4.0 s[/tex], so keeping in mind that the torque is in the same direction of the initial angular speed of the object (therefore, the variation of angular momentum should be positive), we have
[tex]\Delta L = \tau \Delta t = (5.0 Nm)(4.0 s)=20 Nms[/tex]
Lanuel

The change in angular momentum of the wheel is equal to [tex]20 \;Kgm^2/s[/tex].

Given the following data:

  • Rotational inertia = 2.0 [tex]kgm^2[/tex]
  • Angular velocity = 6.0 rad/s
  • Torque = 5.0 Nm
  • Time = 4 seconds

To calculate the change in angular momentum of the wheel:

Mathematically, the change in angular momentum is given by this formula:

[tex]\Delta M = \tau t[/tex]

Where:

  • [tex]\Delta M[/tex] is the change in angular momentum.
  • [tex]\tau[/tex] is the torque.
  • t is the time measured in seconds.

Substituting the given parameters into the formula, we have;

[tex]\Delta M = 5.0\times 4.0\\\\\Delta M =20 \;Kgm^2/s[/tex]

Read more on angular momentum here: https://brainly.com/question/13822610

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