A 10-kg disk-shaped flywheel of radius 9.0 cm rotates with a rotational speed of 320 rad/s. Part A Determine the rotational momentum of the

Question

A 10-kg disk-shaped flywheel of radius 9.0 cm rotates with a rotational speed of 320 rad/s. Part A Determine the rotational momentum of the flywheel. Express your answer to two significant figures and include the appropriate units. Part B With what magnitude rotational speed must a 10-kg solid sphere of 9.0 cm radius rotate to have the same rotational momentum as the flywheel? Express your answer to two significant figures and include the appropriate units.

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1 year 2021-09-04T01:28:59+00:00 1 Answers 1 views 0

(A). The rotational momentum of the flywheel is 12.96 kg m²/s.

(B). The rotational speed of sphere is 400 rad/s.

Explanation:

Given that,

Mass of disk = 10 kg

Rotational speed = 320 m/s

(A). We need to calculate the rotational momentum of the flywheel.

Using formula of momentum

$$L=I\omega$$

$$L=\dfrac{1}{2}mr^2\omega$$

Put the value into the formula

$$L=\dfrac{1}{2}\times10\times(9.0\times10^{-2})^2\times320$$

$$L=12.96\ kg m^2/s$$

(B). Rotation momentum of sphere is same rotational momentum of the  flywheel

We need to calculate the magnitude of the rotational speed of sphere

Using formula of rotational momentum

$$L_{sphere}=L_{flywheel}$$

$$I\omega_{sphere}=I\omega_{flywheel}$$

$$\omega_{sphere}=\dfrac{I\omega_{flywheel}}{I_{sphere}}$$

$$\omega_{sphere}=\dfrac{I\omega_{flywheel}}{\dfrac{2}{5}mr^2}$$

Put the value into the formula

$$\omega_{sphere}=\dfrac{12.96}{\dfrac{2}{5}\times10\times(9.0\times10^{-2})^2}$$

$$\omega_{sphere}=400\ rad/s$$

Hence, (A). The rotational momentum of the flywheel is 12.96 kg m²/s.

(B). The rotational speed of sphere is 400 rad/s.