Question

A carousel is (more or less) a disk of mass, 15,000 kg, with a radius of 6.14. What torque must be applied to create an angular acceleration of 0.0500 rad/s^2?round to 3 significant figures

(Plssss help me im suffering from severe brainrot)

Answer 1

To calculate the torque required to create an angular acceleration, we can use the formula:

Torque = Moment of Inertia × Angular Acceleration

The moment of inertia of a disk can be calculated using the formula:

Moment of Inertia = (1/2) × Mass × Radius^2

Given:

Mass = 15,000 kg

Radius = 6.14 m

Angular Acceleration = 0.0500 rad/s^2

First, calculate the moment of inertia:

Moment of Inertia = (1/2) × Mass × Radius^2

Moment of Inertia = (1/2) × 15,000 kg × (6.14 m)^2

Next, calculate the torque:

Torque = Moment of Inertia × Angular Acceleration

Torque = Moment of Inertia × 0.0500 rad/s^2

Now, let's plug in the values and calculate:

Moment of Inertia = (1/2) × 15,000 kg × (6.14 m)^2

Moment of Inertia ≈ 283,594.13 kg·m^2

Torque = 283,594.13 kg·m^2 × 0.0500 rad/s^2

Torque ≈ 14,179.71 N·m

Rounding to three significant figures, the torque required to create an angular acceleration of 0.0500 rad/s^2 is approximately 14,180 N·m.

`\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}`

♥️
`\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}`