What is the linear speed of a point on the rim of a pulley with a 50 cm diameter driven at 960 r/min?

To determine the linear speed of a point on the rim of a pulley, you can use the formula that relates rotational speed and linear speed. The linear speed ( v ) can be calculated as:

[

v = r \cdot \omega

]

where ( r ) is the radius of the pulley and ( \omega ) is the angular velocity in radians per second.

First, convert the pulley diameter to radius. With a 50 cm diameter, the radius ( r ) is:

[

r = \frac{50 \text{ cm}}{2} = 25 \text{ cm} = 0.25 \text{ m}

]

Next, convert the rotational speed from revolutions per minute (r/min) to radians per second. Since one revolution is ( 2\pi ) radians and there are 60 seconds in a minute, the conversion is:

[

\omega = 960 \text{ r/min} \cdot \frac{2\pi \text{ rad}}{1 \text{ revolution}} \cdot \frac{1 \text{ min}}{60 \text{ s}}

]

Calculating that gives:

[