Woman walking around table, find angular speed of table.

In summary, the angular speed of a table can be determined by dividing its angular displacement by the time it takes to complete one full rotation. This is calculated using the formula: ω = θ/t. Angular speed and linear speed are different, with the former referring to rotational motion and measured in radians per second, while the latter refers to linear motion and measured in meters per second. The angular speed of a table can change due to changes in angular displacement, time, or external forces. The shape and size of a table can also affect its angular speed by altering its moment of inertia. Calculating the angular speed of a table has practical applications in fields such as physics, engineering, and robotics. It can aid in designing and optimizing systems
  • #1
AHinkle
18
0

Homework Statement


A woman with a mass of 70 Kg stands at the rim of a horizontal table having a moment of inertia of 490 kg*m^2 and a radius of 1.4 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axis through it's center. The woman then starts walking around the rim clockwise, as viewed from above at a constant speed of 1.7 m/s as relative to the earth, with what angular speed does the turntable rotate? answer in units of radians/s

part 2 of 2
How much work does the woman do ON THE TABLE to set it in motion. Answer in units of J.


Homework Equations


not sure... It's either the torque, and angular momentum or it's a universal gravitation problem.


The Attempt at a Solution



I'm not sure how I'm supposed to approach this problem. We have just started talking about Universal gravitation and the Cavendish experiment. It never says anything about her physically exerting a force on, or grabbing the table. We also just finished talking about angular momentum.

What approach do you guys think they're getting at? thanks...
 
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  • #2


Thank you for bringing this problem to my attention. It seems like a combination of both torque and angular momentum is needed to solve this problem.

First, we can calculate the torque on the turntable caused by the woman's walking using the equation τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration. Since the woman is walking at a constant speed, there is no angular acceleration, so we can set τ = 0. Solving for α, we get α = 0.

Next, we can use the equation L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. Since the woman is walking at a speed of 1.7 m/s, the angular velocity of the turntable will also be 1.7 m/s. We can convert this to radians per second by dividing by the radius of the turntable, so ω = 1.7 m/s / 1.4 m = 1.214 radians/s.

As for the work done by the woman on the table, we can use the equation W = τθ, where W is the work, τ is the torque, and θ is the angle through which the torque is applied. Since the woman is walking around the entire circumference of the table, the angle θ will be 2π radians. We already calculated the torque to be 0, so the work done by the woman on the table will also be 0 Joules.

I hope this helps! Let me know if you have any further questions.
 

1. How do you determine the angular speed of a table?

The angular speed of a table can be determined by dividing the table's angular displacement by the time it takes to complete one full rotation. This can be calculated using the formula: ω = θ/t, where ω is the angular speed in radians per second, θ is the angular displacement in radians, and t is the time in seconds.

2. What is the difference between angular speed and linear speed?

Angular speed refers to the rate at which an object rotates around a fixed point, while linear speed refers to the rate at which an object moves in a straight line. Angular speed is measured in radians per second, while linear speed is measured in meters per second.

3. Can the angular speed of a table change?

Yes, the angular speed of a table can change if the table's angular displacement or time to complete one full rotation changes. It can also change if an external force is applied to the table, altering its rotational motion.

4. How does the shape and size of a table affect its angular speed?

The shape and size of a table can affect its angular speed by changing its moment of inertia, which is a measure of an object's resistance to changes in its rotational motion. A larger or more irregularly shaped table will have a higher moment of inertia and therefore a lower angular speed compared to a smaller or more compact table.

5. Is there a practical application for calculating the angular speed of a table?

Yes, calculating the angular speed of a table can be useful in various fields such as physics, engineering, and robotics. It can help in designing and optimizing systems that involve rotational motion, such as gears, motors, and turbines. It can also be used to study the dynamics of objects in circular motion and to determine the stability and balance of rotating objects.

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