Question

question 12
use the following to answer questions 12 thru 16.
a rowing machine consists of a solid disk with a radius of 25-cm and a mass of 15-kg. an athlete pulls on the attached cable with a force of 12-newtons and causes the disk to accelerate as shown below. if the disk starts from rest, determine the disk’s moment of inertia.

Explanation:

Step1: Recall the formula for moment of inertia of a solid disk

The moment of inertia \( I \) of a solid disk (or a solid cylinder) about its central axis is given by the formula \( I = \frac{1}{2} M R^2 \), where \( M \) is the mass of the disk and \( R \) is its radius.

Step2: Identify the given values

We are given:

• Mass of the disk, \( M = 15 \, \text{kg} \)
• Radius of the disk, \( R = 25 \, \text{cm} \). First, we need to convert the radius from centimeters to meters because the SI unit of length is meters. Since \( 1 \, \text{m} = 100 \, \text{cm} \), we have \( R = \frac{25}{100} \, \text{m} = 0.25 \, \text{m} \).

Step3: Substitute the values into the formula

Substitute \( M = 15 \, \text{kg} \) and \( R = 0.25 \, \text{m} \) into the formula \( I = \frac{1}{2} M R^2 \):

$$
LATEXBLOCK0
$$

Answer:

The moment of inertia of the disk is \( \boldsymbol{0.46875 \, \text{kg·m}^2} \) (or it can be written as \( \frac{15}{32} \, \text{kg·m}^2 \) if we prefer a fractional form, but the decimal form is also correct).