Question

After the torque has been applied for 0.3 s, what are the magnitude and direction of the angular momentum about the center of the disk?

Answer 1

The magnitude and direction of the angular momentum about the center of the disk is 0.996 kgm²/s.

Angular acceleration of the disk

The angular acceleration of the disk is determined by applying the principle of conservation of angular momentum as shown below;

Fr = Iα

α = Fr/I

Where;

• I is the moment of inertia of the solid disk

I = ¹/₂MR²

I = ¹/₂ x (0.5) x (0.08)²

I = 1.6 x 10⁻³ kgm²

$\alpha = \frac{14 \times 0.22}{1.6\times 10^{-3}}\\\\\alpha = 1,925 \ rad/s^2$

Final angular velocity of the disk

ωf = ωi + αt

ωf = 45 + (1925 x 0.3)

ωf = 622.5 rad/s

Angular momentum

L = Iω

L = (1.6 x 10⁻³) x (622.5)

L = 0.996 kgm²/s

Thus, the magnitude and direction of the angular momentum about the center of the disk is 0.996 kgm²/s.

The complete question is below:

A uniform solid disk with radius 8 cm has mass 0.5 kg (moment of inertia I = (1/2)MR²). A constant force 14 N is applied as shown. At the instant shown, the amount of string that has wound off the disk is d = 22 cm, and the angular velocity of the disk is 45 radians/s into the page.

Learn more about angular momentum here: brainly.com/question/7538238