A pair of belted pulleys have diameters of 20 inch and 16 inch respectively.If the larger pulley turns at 2000 rpm, how fast will the smaller pulley turn.
speed at outer radius is the same
w1 * r1 = w 2 * r 2
where w is radians/second
so
2000 * 20/16
Well, my friend, it seems we have a case of pulley proportions! Let's get our math clown hats on and solve this conundrum.
The speed of pulleys is determined by the ratio of their diameters. In this case, the larger pulley has a diameter of 20 inches, and the smaller pulley has a diameter of 16 inches.
To find the speed of the smaller pulley, we can use the following formula:
Speed of smaller pulley = (Diameter of larger pulley / Diameter of smaller pulley) * Speed of larger pulley
So, plugging in the numbers, we have:
Speed of smaller pulley = (20 inches / 16 inches) * 2000 rpm
Speed of smaller pulley = 1.25 * 2000 rpm
Now, let me whip out my clown-calculator for this one...
*Does some quick calculations*
Voila! The speed of the smaller pulley will be 2500 rpm.
So, my friend, the smaller pulley will be spinning around at 2500 rpm, ready to tackle any circus act that comes its way!
To find the speed at which the smaller pulley will turn, we can use the concept of pulley ratios. The ratio of the pulley speeds is inversely proportional to the ratio of their diameters.
The pulley ratio is given by:
Pulley Ratio = (Diameter of Larger Pulley) / (Diameter of Smaller Pulley)
In this case, the diameter of the larger pulley is 20 inches, and the diameter of the smaller pulley is 16 inches. Plugging in these values, we get:
Pulley Ratio = 20 / 16 = 1.25
This means that for every 1 revolution of the larger pulley, the smaller pulley will make 1.25 revolutions.
Since the larger pulley is turning at 2000 rpm (revolutions per minute), we can calculate the speed of the smaller pulley by multiplying the pulley ratio by the speed of the larger pulley:
Speed of Smaller Pulley = Pulley Ratio * Speed of Larger Pulley
Speed of Smaller Pulley = 1.25 * 2000 = 2500 rpm
Therefore, the smaller pulley will turn at a speed of 2500 rpm.
To determine how fast the smaller pulley will turn, we can use the formula for the relationship between the speeds of two rotating objects connected by a belt or chain. This relationship, known as the belt speed formula, is given by:
Speed of larger pulley * Diameter of larger pulley = Speed of smaller pulley * Diameter of smaller pulley
In this case, we are given that the larger pulley turns at a speed of 2000 revolutions per minute (rpm), and the diameters of the two pulleys are 20 inches and 16 inches, respectively.
Let's plug in the given values into the formula and solve for the speed of the smaller pulley:
Speed of larger pulley * 20 inches = Speed of smaller pulley * 16 inches
2000 rpm * 20 inches = Speed of smaller pulley * 16 inches
40,000 inches per minute = Speed of smaller pulley * 16 inches
Now, let's isolate the speed of the smaller pulley:
Speed of smaller pulley = 40,000 inches per minute / 16 inches
Speed of smaller pulley = 2500 inches per minute
Therefore, the smaller pulley will turn at a speed of 2500 inches per minute.