Questions: Find the linear speed ν for the following. a point on the edge of a flywheel of radius 2 m , rotating 44 times per min The linear speed ν for a point on the edge of a flywheel of radius 2 m , rotating 44 times per min is (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)

$Find the linear speed ν for the following. a point on the edge of a flywheel of radius 2 m , rotating 44 times per min The linear speed ν for a point on the edge of a flywheel of radius 2 m , rotating 44 times per min is (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)$

Transcript text: Find the linear speed $\nu$ for the following. a point on the edge of a flywheel of radius 2 m , rotating 44 times per min The linear speed $\nu$ for a point on the edge of a flywheel of radius 2 m , rotating 44 times per min is $\square$ $\square$ (Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

Solution

Solution Steps

Step 1: Understand the Problem

We need to find the linear speed $\nu$ of a point on the edge of a flywheel. The flywheel has a radius of 2 meters and rotates 44 times per minute.

Step 2: Calculate the Circumference of the Flywheel

The circumference $C$ of a circle (or flywheel in this case) is given by the formula: \[ C = 2\pi r \] where $r$ is the radius. Substituting $r = 2$ meters, we get: \[ C = 2\pi \times 2 = 4\pi \text{ meters} \]

Step 3: Calculate the Linear Speed

The linear speed $\nu$ is the distance traveled per unit of time. Since the flywheel rotates 44 times per minute, the point on the edge travels 44 circumferences per minute. Therefore, the linear speed is: \[ \nu = 44 \times 4\pi = 176\pi \text{ meters per minute} \]