Rpm related to velocity and diameter

In summary, to determine RPM when given velocity and the radius or diameter of a circle, you can use the formula 1/T where T is the time it takes to travel one revolution. This can be calculated by dividing the distance traveled in one revolution (2Pi.r) by the speed (v). Then, to get the RPM, you can take the reciprocal of T. For example, if the radius is 1.5 ft and the speed is 95.34 ft/s, the RPM would be 10.121. This method was confirmed to be correct.
  • #1
cgaday
58
0
How do you determine RPM when given your velocity and the radius or diameter of the cirlcle?

thanks in advance.
 
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  • #2
One circumference is 2Pi.r. That's distance traveled in one revolution.
If you travel at speed v, then the time T it takes to travel that distance = distance divided by speed.
Finally, if it takes T seconds for one revolution, you do 1/T revolutions per second.
Put it all together to get the answer.
 
  • #3
so for r = 1.5 ft therefore 2pi(1.5) = 9.42 feet
speed equals 95.34 ft/s

T = distance/speed = 9.42 ft/ 95.34 ft per sec = .0988

1/T = 1/.0988 = 10.121 rev/s

IS this correct.
 
  • #4
Yes, that looks fine to me. :)
 
  • #5


RPM, or revolutions per minute, is a measurement of rotational speed. It tells us how many full rotations a circular object makes in one minute. The relationship between RPM, velocity, and diameter is based on the formula v = ωr, where v is the linear velocity, ω is the angular velocity (in radians per minute), and r is the radius or half of the diameter of the circle.

To determine the RPM when given velocity and the radius or diameter of the circle, we can rearrange the formula to ω = v/r and then convert ω to RPM by multiplying it by 60 seconds (since there are 60 seconds in a minute) and dividing by 2π (since there are 2π radians in a full rotation). The final formula would be RPM = (v/r) * (60/2π).

For example, if we have a circular object with a diameter of 10 cm and a velocity of 20 cm/s, the radius would be 5 cm (half of the diameter). Plugging these values into the formula, we get RPM = (20/5) * (60/2π) = 240/2π ≈ 38.2 RPM.

It is important to note that this formula assumes a constant velocity and a perfect circular motion. In real-world scenarios, there may be variations in velocity and the circular motion may not be perfect, which can affect the accuracy of the calculated RPM. Other factors such as friction and external forces may also play a role in determining the RPM of a rotating object.
 

FAQ: Rpm related to velocity and diameter

What is the relationship between RPM, velocity, and diameter?

The relationship between RPM (revolutions per minute), velocity, and diameter is based on rotational speed and the distance traveled by the rotating object. RPM is a measure of how many full rotations a spinning object makes in one minute, while velocity is the speed at which the object is traveling in a straight line. The diameter of the object also plays a role in determining its speed, as a larger diameter will cover more distance per rotation than a smaller diameter.

How does changing the RPM affect the velocity and diameter of a rotating object?

Increasing the RPM of a rotating object will increase its velocity, as it will make more rotations in a specific amount of time. However, the diameter of the object will also be affected. If the RPM is increased, the diameter must decrease in order for the object to maintain its speed. Similarly, decreasing the RPM will decrease the velocity and the diameter must increase.

What is the formula for calculating RPM?

The formula for calculating RPM is: RPM = (60 x velocity) / (2 x π x radius). This formula takes into account the velocity of the object, the radius of the object, and the constant value of π (pi). It is important to note that the radius used in this formula is the distance from the center of the object to the edge, not the full diameter.

How does the diameter of a rotating object affect its RPM and velocity?

As mentioned before, the diameter of a rotating object has a direct impact on its RPM and velocity. A larger diameter will result in a higher RPM and velocity, while a smaller diameter will result in a lower RPM and velocity. This is because a larger diameter will cover more distance per rotation, resulting in a higher speed.

How do RPM and velocity affect the performance of a rotating object?

RPM and velocity are crucial factors in determining the performance of a rotating object. A higher RPM and velocity can result in faster and more efficient rotation, while a lower RPM and velocity may result in slower and less efficient rotation. In some cases, the performance of a rotating object may also be affected by the diameter, as a larger diameter can provide more torque and power to the object.

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