# Calculating final rotational speed from angular velocity

• Anmol Dubey
In summary, the conversation discusses the conversion of 1.5 rev/s to rad/s and the relationship between the quantities in the relevant equation. It is determined that the quantities I(final), I(initial), w(final), and w(initial) are related through the conservation of angular momentum. If I(final) is increased by a factor of 3, w(final) is decreased by a factor of 3 to maintain the conservation of angular momentum. The conversation concludes with confirmation of the correct solution.
Anmol Dubey
Homework Statement
An ice skater is spinning with a rotational speed of 1.5 rev/s. When he extends his arms and one leg, his rotational inertia increases by a factor of three. What is his final rotational speed?
Relevant Equations
Angular momentum is conserved
L = Iw
L (final) = L (initial)
I(initial)*w(initial) = I(final)*w(final)
I have no idea how to go about this. Any help would be appreciated thanks :)
Edit: I converted the 1.5 rev/s to rad/s = 9.4 rad/s

Last edited:
What do you know about the quantities in your last relevant equation?

Anmol Dubey
Orodruin said:
What do you know about the quantities in your last relevant equation?
Like I = mr2?
w = Δθ/Δt
I didn't get what you mean by quantities

Anmol Dubey said:
Like I = mr2?
w = Δθ/Δt
I didn't get what you mean by quantities
No, what does the problem formulation tell you about these quantities:
I(final)
I(initial)
w(final)
w(initial)

Anmol Dubey
Orodruin said:
No, what does the problem formulation tell you about these quantities:
I(final)
I(initial)
w(final)
w(initial)
Since L is conserved
If I(final) is increased by a factor of 3, the w(final) is decreased by a factor of 3 so that L(final) = L(initial)
I(initial)*w(initial) = I(final)*w(final)
x*9.4 rad/s = 3x * w
so w(final) = 9.4 rad/s / 3
Is that correct?

Anmol Dubey said:
Is that correct?
Yes.

Anmol Dubey
Orodruin said:
Yes.
Thank you for helping

## 1. What is the formula for calculating final rotational speed from angular velocity?

The formula is final rotational speed = angular velocity x radius, where angular velocity is measured in radians per second and radius is measured in meters.

## 2. How do you convert angular velocity from revolutions per minute to radians per second?

To convert from revolutions per minute (rpm) to radians per second (rad/s), you can use the formula: angular velocity (rad/s) = 2π x angular velocity (rpm) / 60. This is because there are 2π radians in one revolution and 60 seconds in one minute.

## 3. Can you calculate final rotational speed without knowing the radius?

No, the radius is a necessary component in the formula for calculating final rotational speed from angular velocity. Without knowing the radius, the calculation cannot be completed.

## 4. What is the difference between angular velocity and linear velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed point, while linear velocity is a measure of how fast an object is moving in a straight line. Angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

## 5. How does changing the angular velocity affect the final rotational speed?

Increasing the angular velocity will result in a higher final rotational speed, while decreasing the angular velocity will result in a lower final rotational speed. This is because the final rotational speed is directly proportional to the angular velocity.

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