# Problem with old and New angular speed help me please

• coey
In summary: The final angular speed is 0.402 rad/s.In summary, a student is trying to solve a problem involving a freely rotating stool and weights. They initially have an angular speed of 0.746 rad/s and a moment of inertia of 2.92 kg · m2. The student pulls the weights closer to the axis of rotation and needs to find the new angular speed and kinetic energy before and after. By using conservation of angular momentum and the formula L = p × r, the student can find the new angular speed to be 0.402 rad/s.
coey
I'm kinda having trouble figuring out this problem... i was thinking of doing a system of equations to relate the present angular and new angular speed but that didn't really get me anywhere because i wasn't really including all the variables in the problem... that and i couldn't simplify it down to one variable to solve for. If anyone could help me out i'd appreciate it a lot.

A student sits on a freely rotating stool holding two weights, each of mass 2.92 kg. When his arms are extended horizontally, the weights are 1.09 m from the axis of rotation and he rotates with an angular speed of 0.746 rad/s.

The moment of inertia of the student plus stool is 2.92 kg · m2 and is assumed to be constant. The student pulls the weights in horizontally to a position 0.307 m from the rotation axis.

Question: Find the new angular speed and find the kinetic energy before and after he pulls the weight inward.

Whats changing here is the moment of inertia of the weights. They are originally at distance 1.09m and are contracted to 0.307m. Find this new moment of inertia.

Then since momentum is conserved in the system, you can find the new angular speed by:

$$I_i\omega_i = I_f\omega_f$$ solved for $$\omega_f$$

Just to concur with whozum:
You need to use conservation of angular momentum:
$$L_i = L_f$$
Where:
$$L = p\times r$$

## 1. What is angular speed?

Angular speed is a measure of how fast an object is rotating around a fixed axis. It is measured in radians per unit of time, such as radians per second.

## 2. What is the problem with old and new angular speed?

The problem with old and new angular speed is that there may be inconsistencies or discrepancies between the two measurements, causing confusion or errors in calculations.

## 3. How do I calculate angular speed?

Angular speed can be calculated by dividing the change in angular displacement by the change in time. It can also be calculated by dividing linear speed by the radius of the circular motion.

## 4. How does angular speed relate to linear speed?

Angular speed and linear speed are related by the formula v = ωr, where v is linear speed, ω is angular speed, and r is the radius of the circular motion. This means that as the radius increases, the linear speed also increases at a proportional rate.

## 5. Can angular speed change over time?

Yes, angular speed can change over time. This is known as angular acceleration, which is caused by a change in the angular velocity or direction of an object. It is measured in radians per second squared.

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