How Do You Calculate the Velocity of a Point on a Rotating Disc?

In summary, in order to find the velocity v of a general point on a plate rotating at 800 rpm with a radius of r meters from the center, one can use the equation v = (2 pi r) / T, where T is the period of the rotation, which can be found by taking the inverse of the frequency (f = 40/3 rps). This results in a velocity of (80 pi r) / 3 m/sec.
  • #1
JJK1503
12
0

Homework Statement



Find the velocity v of a general point on a plate rotating at 800 rpm which is r meters from the center.

This is literally a copy and paste job.

Homework Equations



period = T = 1 / f ; f = frequency

The Attempt at a Solution



This is what I did please tell me if it is correct

800 rpm = 40 / 3 rps = f

T = 1 / f = 3 / 40

v = distance / time = (2 pi r) / (3 / 40) = (80 pi r) / 3
 
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  • #2
That is correct.
You could also have seen that 40/3 rps can be directly translated into a speed by replacing the r in rps with the distance covered in 1 revolution (2 pi r).
That would give you the same result ##\frac{80 \pi r}{ 3}##m/sec.
 
  • #3
Yes, that works. You need to carry the "seconds" unit through to the end though. The period T has seconds as its unit.

Otherwise you'll end up with a "velocity" with units of distance rather than distance/time.
 
  • #4
RUber said:
That is correct.
You could also have seen that 40/3 rps can be directly translated into a speed by replacing the r in rps with the distance covered in 1 revolution (2 pi r).
That would give you the same result ##\frac{80 \pi r}{ 3}##m/sec.
Awesome! Thank you.
 
  • #5
gneill said:
Yes, that works. You need to carry the "seconds" unit through to the end though. The period T has seconds as its unit.

Otherwise you'll end up with a "velocity" with units of distance rather than distance/time.
Ohh... I see. Thank you
 

Related to How Do You Calculate the Velocity of a Point on a Rotating Disc?

1. What is the formula for calculating the velocity of a rotating disc?

The formula for calculating the velocity of a rotating disc is v = ωr, where v is the velocity, ω is the angular velocity, and r is the radius of the disc.

2. How does the radius of a rotating disc affect its velocity?

The radius of a rotating disc directly affects its velocity. As the radius increases, the velocity also increases. This is because the linear velocity of a point on the disc's edge is directly proportional to the radius.

3. Is the velocity of a rotating disc constant?

No, the velocity of a rotating disc is not constant. The linear velocity of each point on the disc's edge is constantly changing as it rotates. However, the angular velocity, which is the rate of change of the disc's angle, remains constant.

4. How does the mass of a rotating disc affect its velocity?

The mass of a rotating disc does not directly affect its velocity. However, a disc with a larger mass may require more energy to rotate at a certain velocity compared to a disc with a smaller mass.

5. Can the velocity of a rotating disc be negative?

Yes, the velocity of a rotating disc can be negative. This occurs when the disc is rotating in the opposite direction of the chosen reference point. In this case, the velocity is considered negative because it is moving in the opposite direction of the positive chosen reference point.

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