How Does a Cockroach Affect the Angular Speed of a Lazy Susan?

In summary, the conversation discusses a scenario where a cockroach of mass m is running counterclockwise on a lazy Susan of radius R and rotational inertia I, which is turning clockwise with an angular speed wo. The cockroach eventually stops when it finds a bread crumb on the rim. The conversation then explores the relationship between the cockroach's linear speed and the lazy Susan's angular speed. It is suggested to use conservation of angular momentum to calculate the angular speed of the lazy Susan after the cockroach stops, and to assume that the lazy Susan has no angular momentum when the cockroach gets on it. The formula w= (mRv - Iwo) / (I + mR^2) is mentioned as a way
  • #1
Oblio
398
0
A cockroach of mass m runs counterclockwise around the rim of a lazy Susan (a circular disc mounted on a vertical axle) of radius R and rotational inertia I with frictionless bearings. The cockroach's speed relative to the Earth is v, where as the lazy Susan turns clockwise with angular speed wo. The cockroach finds a bread crumb on the rim and, or course stops. a) what is the angular speed of the lazy susan after cockroach stops. b.) Is mechanical energy conserved?


I'm not sure how to relate the cockroach's linear speed with the angular speed of the disc...

I'd love any help..
thanks!
 
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  • #2
Use conservation of angular momentum... take clockwise positive... counterclockwise negative... what is the angular momentum of the cockroach before it stops... what is the angular momentum of the lazy Susan before the cockroach stops?

angular momentum afterwards the roach stops equals angular momentum before...
 
  • #3
Try and use conservation of angular momentum - assume that the LS has none when the cc gets on it.
 
  • #4
How do I manage to use a linear speed of (cockroach) when its spinning though? isn't rotational motion acceleration?

It doesn't make sense to me...
 
  • #5
The cockroach has both linear momentum and angular momentum. Given the first and the distance from the axis, you can calculate the second. (Treat the cockroach as a point mass.)
 
  • #6
w= ( mRv - Iwo ) / ( I + mR^2 )
 

Related to How Does a Cockroach Affect the Angular Speed of a Lazy Susan?

1. What is rotational inertia in relation to a cockroach?

Rotational inertia refers to the resistance of an object to rotational motion. In the case of a cockroach, this refers to its ability to resist changes in its rotation while moving.

2. How does rotational inertia affect a cockroach's movement?

The rotational inertia of a cockroach plays a crucial role in its movement. It allows the cockroach to maintain stability and control while navigating through its environment.

3. Can the rotational inertia of a cockroach be measured?

Yes, the rotational inertia of a cockroach can be measured using various scientific techniques such as video analysis or motion tracking devices.

4. Are there any factors that can affect the rotational inertia of a cockroach?

Yes, the rotational inertia of a cockroach can be affected by its size, shape, and mass distribution. Additionally, external factors such as air resistance and surface friction can also impact its rotational inertia.

5. How does the rotational inertia of a cockroach compare to other animals?

The rotational inertia of a cockroach is relatively low compared to larger animals, such as elephants, due to its small size and streamlined body shape. However, it is still an important factor in its movement and survival.

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