A pulley having a diameter of 36 cm is turned by a belt that moves at the rate of 5m/sec . How many revolutions does the pulley make per/sec?
circumference of pulley = 36π cm
5 m = 500 cm
so we need 500/36π revolutions/sec
or appr. 4.42 revs/sec
To find the number of revolutions the pulley makes per second, we need to convert the belt's linear velocity to angular velocity.
The equation to calculate angular velocity is:
Angular velocity (ω) = linear velocity (v) / radius (r)
First, we need to convert the diameter of the pulley to its radius:
Radius (r) = diameter / 2
= 36 cm / 2
= 18 cm
= 0.18 m
Now, we can substitute the values into the equation:
Angular velocity (ω) = 5 m/s / 0.18 m
= 27.78 rad/s
To convert angular velocity to revolutions per second, we need to use the following conversion factor:
1 revolution = 2π radians
So, the number of revolutions per second is:
Revolutions per second = ω / 2π
= 27.78 rad/s / 2π
≈ 4.42 revolutions per second
Therefore, the pulley makes approximately 4.42 revolutions per second.
To find the number of revolutions the pulley makes per second, we need to know the circumference of the pulley.
The circumference of a circle can be found using the formula: circumference = 2π * radius.
In this case, the diameter of the pulley is given as 36 cm. The radius of the pulley can be calculated by dividing the diameter by 2: radius = diameter / 2 = 36 cm / 2 = 18 cm.
Now, we convert the radius from centimeters to meters, since the belt's speed is given in meters per second: radius = 18 cm * (1 m / 100 cm) = 0.18 m.
Using the circumference formula, we can find the circumference of the pulley: circumference = 2π * radius = 2 * π * 0.18 m ≈ 1.13 m.
Finally, to determine the number of revolutions per second, we divide the belt's speed (5 m/s) by the circumference of the pulley: revolutions per second = speed / circumference = 5 m/s / 1.13 m ≈ 4.42 revolutions per second.
Therefore, the pulley makes approximately 4.42 revolutions per second.