Conceptual Physics

Draw a diagram

Variables

What is the strategy?

1. Calculate the moment of inertia of the system: the sum of the moments for the children, and the moment of the plank.


2. Calculate the net torque by summing the torques created by each child. The torques of the left and right sides of the plank cancel, so
   you do not have to consider them.


3. Divide the net torque by the moment of inertia to determine the initial angular acceleration.

Physics principles and equations

We will use the definitions of torque and moment of inertia.

IJ = rF sin ș,I = Ȉmr^2

To calculate the moments of inertia of the children, we consider the mass of each to be concentrated at one point.

The plank can be considered as a slab rotating on an axis parallel to an edge through the center, with moment of inertia

The equation relating net torque and moment of inertia is Newton's second law for rotation,

ȈIJ = IĮ

Step-by-step solution

First, we add the moments of inertia for the two children and the seesaw plank. The sum of these values equals the system's moment of inertia.

mass of seesaw plank mS = 36.5 kg

seesaw plank’s moment of inertia IS

girl boy

mass mG = 42.8 kg mB = 55.2 kg

distance from axis rG = 2.13 m rB = 1.51 m

moment of inertia IG IB

Step Reason

1. I = IG + IB + IS total moment is sum

2. I = mGrG^2 + mBrB^2 + IS definition of moment of inertia

3. moment of slab

4. enter values

5. I = 379 kg·m^2 evaluate

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