Rotational Motion: Calculating Time to Reach 750 RPM

In summary, the question asks about the time it takes for a 1.5 hp motor to drive a 4.5 kg disk with a diameter of 0.4 m from rest to a speed of 750 rpm. The relevant equations are angular momentum and torque. The student is unsure of how to find time without distance or acceleration and has attempted to solve for acceleration, but is unsure of how horsepower relates to torque. They also ask about the energy of the disk at operating speed and the relationship between power, energy, and time.
  • #1
hannah12345
2
0

Homework Statement


A 1.5 hp motor drives a machine disk having a mass of 4.5 kg and a diameter of .4 m from rest to a speed of 750 rpm. How long does it take to reach the operating speed?

Homework Equations


angular momentum
torque

The Attempt at a Solution


I'm not really sure where to start with this problem. I don't know how to find time without distance or acceleration. I tried solving for acceleration but I'm not sure how horsepower relates to torque.
 
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  • #2
How much energy will the disk have at operating speed?
 
  • #3
How would I use that to find time?
 
  • #4
hannah12345 said:
How would I use that to find time?
What is the relationship between power, energy and time?
 

1. How is rotational motion defined?

Rotational motion is the movement of an object around a fixed axis, where every point on the object moves in a circular path at the same time and with the same angular velocity.

2. What is the formula for calculating time to reach a certain RPM?

The formula for calculating time to reach a certain RPM is: time = (750 RPM x 60 seconds) / 750 revolutions = 60 seconds.

3. How does the mass of an object affect its rotational motion?

The mass of an object does not directly affect its rotational motion. However, the distribution of mass around the axis of rotation, known as the moment of inertia, can affect the object's rotational acceleration.

4. Is the time to reach 750 RPM affected by the initial velocity?

No, the time to reach 750 RPM is not affected by the initial velocity. This is because the formula for calculating time only takes into account the final RPM and the number of revolutions.

5. How does the radius of rotation affect the time to reach 750 RPM?

The radius of rotation does not directly affect the time to reach 750 RPM. However, it can affect the linear speed of the object, which in turn can affect the rotational speed and thus the time to reach 750 RPM.

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