Rigid body dynamics: falling stick

In summary, the equation that determines whether the rod will stick or slip is Ax= -αRSinθ - uK*N / m. If m = 10kg and L = 100cm with uS = 0.8, uK = 0.7 and initial theta = 30 degrees, the initial acceleration for stick and slip can be calculated using the equation α = -(3/2L)gsinθ.
  • #1
Feodalherren
605
6

Homework Statement


A stick of length L and mass m is falling on a table with kinetic friction uK and static friction uS. Find the equation that determines whether the rod will stick or slip.

If m = 10kg and L = 100cm, uS = 0.8, uK = 0.7 and initial theta = 30 degrees find the initial accel for stick and slip.

Homework Equations


Irod = (1/3)mL^2
M= r x F

The Attempt at a Solution


I'm so stuck.

I made an FBD but as far as I can see, there are no forces in the X-direction, so what exactly makes the thing slip?
 
Last edited:
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  • #2
From my FBD:

Iα = -mg(L/2)Sinθ

then α = -(3/2L)gsinθ

so far so good?
 
  • #3
By which the translational x-acceleration of the rod must be (taking positive x to the left):

Ax= -αRSinθ - uK*N / m

correct?
 
  • #4
Nobody?
 

Related to Rigid body dynamics: falling stick

1. What is rigid body dynamics?

Rigid body dynamics is a branch of mechanics that studies the motion of solid objects, assuming they are rigid and do not deform under the influence of external forces.

2. What is the falling stick problem in rigid body dynamics?

The falling stick problem is a classic problem in rigid body dynamics that involves predicting the motion of a stick as it falls from a vertical position. This problem helps illustrate concepts such as rotational motion, center of mass, and torque.

3. How is the motion of a falling stick determined in rigid body dynamics?

The motion of a falling stick is determined by applying Newton's laws of motion and rotational dynamics. The stick's center of mass, mass distribution, and initial conditions such as its position and velocity are also important factors in predicting its motion.

4. What factors affect the motion of a falling stick in rigid body dynamics?

The motion of a falling stick is affected by several factors, including its length, mass distribution, initial position and velocity, air resistance, and the gravitational force acting on it.

5. What are some real-world applications of rigid body dynamics?

Rigid body dynamics has many real-world applications, such as predicting the motion of satellites and other objects in space, analyzing the movement of vehicles and aircraft, and understanding the behavior of structures under stress and strain.

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