(UCM) Maximum Rev. Per Minute Using Length and Acceleration

In summary, the (UCM) Maximum Rev. Per Minute Using Length and Acceleration is the highest number of full rotations an object can make per minute while maintaining a constant acceleration and length of its circular path. It is measured in revolutions per minute (rpm) and is affected by the acceleration, length of the circular path, and external forces. The formula for calculating it is: Maximum Rev. Per Minute = (2π * Acceleration * Length)^-1 * 60 seconds. Real-life examples include spinning tops, Ferris wheels, record players, race cars, and fan blades.
  • #1
oziemaster
5
0

Homework Statement



An astronaut rotates at the end of a test machine whose arm has a length of 10m. If the acceleration she experiences must not exceed 5g (g = 10 ms^-2), what is the maximum number of revolutions per minute of the arm?

Homework Equations



T = (2πR)/v

V = (2πR)/T

Ac = V2/r

The Attempt at a Solution



Ac = v2/r

Plug in acceleration given and radius (from length of 10m): 10 = v2/5

5*10 = 50

50 = v2

v = 7.07107

T = 2π*5/7.07107

T = 4.44288 revolutions for 1g

Multiply 4.44288 by 5 = 22.2144 RPM?
 
Last edited:
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  • #2
Hi Oziemaster,

Do you know what "g" is?

ehild
 

Related to (UCM) Maximum Rev. Per Minute Using Length and Acceleration

What is (UCM) Maximum Rev. Per Minute Using Length and Acceleration?

UCM stands for Uniform Circular Motion, which refers to the motion of an object in a circular path at a constant speed. The maximum revolution per minute using length and acceleration is the highest number of full rotations an object can make per minute while maintaining a constant acceleration and length of its circular path.

How is (UCM) Maximum Rev. Per Minute Using Length and Acceleration measured?

The (UCM) Maximum Rev. Per Minute Using Length and Acceleration is measured in revolutions per minute (rpm), which is the number of full rotations an object makes in one minute.

What factors affect the (UCM) Maximum Rev. Per Minute Using Length and Acceleration?

The (UCM) Maximum Rev. Per Minute Using Length and Acceleration is affected by the acceleration of the object, the length of its circular path, and any external forces acting on the object, such as friction or air resistance.

What is the formula for calculating (UCM) Maximum Rev. Per Minute Using Length and Acceleration?

The formula for calculating (UCM) Maximum Rev. Per Minute Using Length and Acceleration is:
Maximum Rev. Per Minute = (2π * Acceleration * Length)^-1 * 60 seconds

What are some real-life examples of (UCM) Maximum Rev. Per Minute Using Length and Acceleration?

Examples of (UCM) Maximum Rev. Per Minute Using Length and Acceleration include the revolutions per minute of a spinning top, a Ferris wheel, or a record player. It can also be used to calculate the maximum rpm of a race car going around a circular track or the rpm of a fan blade spinning at a constant speed.

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