To solve this problem we must apply the concepts related to the torque expressed as a function of the angular acceleration and the moment of inertia as well as the radius and the force. From these two definitions we will seek to find the angular acceleration of the body:
We know that Torque is defined as,
[tex]\tau = I \alpha[/tex]
Here,
I = Moment of Inertia
[tex]\alpha[/tex] = Angular acceleration
And at the same time, the torque is the product between the force and the radius, then we have
[tex]\tau = rF[/tex]
Here,
r = Radius
F = Force
Equation we have,
[tex]rF = I\alpha[/tex]
Rearranging to find the acceleration
[tex]\alpha = \frac{rF}{I}[/tex]
Our values are,
[tex]\text{Rotational Inertia of Disk} = I = 2.0 kg\cdot m^2[/tex]
[tex]\text{Radius of disk} = r = 0.40m[/tex]
[tex]\text{Force} = F = 5.0N[/tex]
Replacing this value at the previous equation
[tex]\alpha = \frac{(0.40m)(5.0N)}{2.0kg\cdot m^2}[/tex]
[tex]\alpha = 1 rad/s^2[/tex]
Therefore the angular acceleration of the disk is [tex]1rad/s^2[/tex]
The angular acceleration of the disk is equal to 1 [tex]rad/s^2[/tex].
Given the following data:
To determine the angular acceleration of the disk:
Mathematically, angular acceleration is given by the formula:
[tex]\alpha = \frac{Fr}{I}[/tex]
Where:
Substituting the given parameters into the formula, we have;
[tex]\alpha =\frac{5 \times 0.4}{2} \\\\\alpha =\frac{2}{2} \\\\\alpha = 1 \;rad/s^2[/tex]
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