Chapter 11: Q9Q (page 458)
Consider a rotating star far from other objects. Its rate of spin stays constant, and its axis of rotation keeps pointing in the same direction. Why?
The rate of spin stays constant, and its axis of rotation keeps pointing in the same direction due to the angular momentum.
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Redo the analysis, calculating torque and angular momentum relative to a fixed location in the ice anywhere underneath the string (similar to the analysis of the meter stick around one end). Show that the two analyses of the puck are consistent with each other.
In Figure 11.96a spherical non-spinning asteroid of mass\(M\)and radius\(R\)moving with speed\({v_1}\)to the right collides with a similar non-spinning asteroid moving with speed\({v_2}\)to the left, and they stick together. The impact parameter is\(d\).Note that\({I_{sphere}} = \frac{2}{5}M{R^2}.\)
After the collision, what is the velocity \({v_{CM}}\) of the center of mass and the angular velocity \(\omega \) about the center of mass? (Note that each asteroid rotates about its own center with this same \(\omega \)).
If you did not already do problem P63 do it now. Also calculate numerically the angle through which the apparatus turns, in radians and degrees.
In Figure 11.95 two small objects each of mass \({m_1}\)are connected by a light weight rod of length \(L.\) At a particular instant the center of mass speed is\({v_1}\) as shown, and the object is rotating counterclockwise with angular speed \({\omega _1}\). A small object of mass \({m_2}\) travelling with speed \({v_2}\) collides with the rod at an angle \({\theta _2}\) as shown, at a distance\(b\)from the center of the rod. After being truck, the mass \({m_2}\) is observed to move with speed \({v_4}\) at angle\({\theta _4}\).All the quantities are positive magnitudes. This all takes place in outer space.
For the object consisting of the rod with the two masses, write equations that, in principle, could be solved for the center of mass speed \({v_3},\) direction \({\theta _3},\) and angular speed \({\omega _3}\)in terms of the given quantities. Sates clearly what physical principles you use to obtain your equations.
Don’t attempt to solve the equations; just set them up.
A rod rotates in the vertical plane around a horizontal axle. A wheel is free to rotate on the rod, as shown in Figure 11.74. A vertical stripe is painted on the wheel remains vertical. Is the translational angular momentum of the wheel relative to location A zero or non-zero? If non-zero, what is its direction? Is the rotational angular momentum of the wheel zero or non-zero? If non-zero, what is its direction? Consider a similar system, but with the wheel welded to the rod (not free to turn). As the rod rotates clock wise, does the stripe on the wheel remain vertical? Is the translational angular momentum of the wheel relatives to location A zero or non-zero? If non-zero, what is its direction? Is the rotational angular momentum of the wheel zero or non-zero? If non-zero, what is its direction?
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