Rotating Systems (College Board AP® Physics 1: Algebra-Based)
Study Guide
Rotating systems
The rotation of a rigid system can be described over time by its:
These are the rotational analogs of the linear variables that describe an object moving in a straight line
Rigid systems
A rigid system is defined as:
A system that holds its shape but in which different points on the system move in different directions during rotation
In linear motion, objects are usually modeled as point particles, which means:
all the mass is located at a single point
the size, shape, and internal configuration are ignored
In rotational motion, objects and systems are modeled as rigid, extended bodies, which means:
the mass is distributed throughout the object (or system)
the size, shape, and internal configuration cannot be ignored
Therefore, a rigid system cannot be modeled as an object
Center of mass
Calculations involving rotating systems can be simplified by considering the motion of the system’s center of mass
If the rotation of a system about an axis can be described by the displacement, velocity, and acceleration of its center of mass, the system may be treated as a single object
For example, the rotation of Earth about its axis may be considered negligible when considering the revolution of Earth about the center of mass of the Earth-Sun system
Worked Example
If the gravitational force between the Earth and the Sun were to stop acting, which of the following statements best describes the resulting motion of the Earth?
A: It would continue revolving around the Sun and rotating on its axis.
B: It would continue rotating on its axis but stop revolving around the Sun.
C: It would stop rotating on its axis but continue revolving around the Sun.
D: It would stop revolving around the Sun and rotating on its axis.
The correct answer is B
Answer:
Step 1: Analyze the scenario
The gravitational force between the Sun and the Earth provides the centripetal force which keeps the Earth orbiting the Sun in uniform circular motion
This force acts at the Earth's center of mass, whereas the rotation of the Earth is about its axis, i.e. at a distance from its center of mass
Step 2: Eliminate incorrect options
If the gravitational force suddenly stopped acting, then there would be no centripetal force
Therefore, the Earth would no longer revolve around the Sun
Instead, it would continue to move along a straight line in whichever direction it was moving at that moment
This eliminates options A and C
Step 3: Deduce the correct option
The gravitational force affects the Earth's center of mass but does not have any effect on its rotational motion
Therefore, the Earth would continue rotating on its axis
Therefore option B is correct
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