A pulley with a diameter of 50cm is driven at 960 r/min. What will be the linear speed, in m/s, of a point on the rim of the pulley?

To determine the linear speed of a point on the rim of the pulley, we can use the formula that relates rotational speed (in revolutions per minute) to linear speed:

[ \text{Linear Speed} (v) = \text{Circumference} \times \text{Revolutions per second} ]

First, we need to calculate the circumference of the pulley. The formula for circumference (C) of a circle is:

[ C = \pi \times d ]

where (d) is the diameter of the pulley. Given that the diameter is 50 cm (or 0.5 m), the circumference is:

[ C = \pi \times 0.5 , \text{m} \approx 1.57 , \text{m} ]

Next, we need to convert the revolutions per minute (r/min) to revolutions per second (r/s):

[ 960 , \text{r/min} = \frac{960}{60} , \text{r/s} = 16 , \text{r/s} ]

Now, we can calculate the linear speed using the previously mentioned linear speed formula:

[ v = C