Question

A stick is resting on a concrete step with 2/5 of its length hanging over the edge. A single ladybug lands on the end of the stick hanging over the edge, and the stick begins to tip. A moment later, a second, identical ladybug lands on the other end of the stick, which results in the stick coming momentarily to rest 41.3° from the horizontal. If the mass of each bug is 3.43 times the mass of the stick and the stick is 18.7 cm long, what is the magnitude of the angular acceleration of the stick at the instant

Answer 1

so first we have to see what tools are best, so \[\frac{ \sum \tau }{ I }=\alpha \] where alpha is the angular acceleration, I is the moment of inertia defined as \[\sum_{i}^{} m_iR_i^2=I\]. and Tau is the net torque on the system

Answer 2

so plug in values known that fit best with each variable in these equations if you can

Answer 3

also remember that the net torque is defined as \[\sum \tau= RF\] and R is the distance perpendicular to the line of force and the axis of rotation which must be fixed in this situation

Answer 4

since the stick is at an angle break the net torque into x/y components like this\[\sum \tau= \sum \tau(x) + \sum \tau(y) \] with \[\sum \tau(x)=RFcos(\theta) \] and \[\sum \tau(y)=RFsin(\theta)\]

Answer 5

and the stick should be tilted upwards and my mistake lady bug number two is on the left

Answer 6

perhaps it's also good to think of the stick as a thin rod(uniform) too, so the moment of inertia of a long uniform rod through end is \[\frac{ 1 }{ 3 } *M*l^2\]

Answer 7

and in this case M=mass of the stick and \[l=.4l_0\]

Answer 8

\[ l_0=18.7cm\]