Friction on an Incline
Tilt the axis so that the x-axis is parallel with the slope - simplifies the math. If you tilt the axis, swap the sin and cos functions if the angle stays the same. If you calculate the new angle, then keep the same sin and cos functions.
Circular Motion
Uniform Circular Motion
- Uniform Circular Motion
- At constant speed, though velocity is changing directions.
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Velocity is at right angles to circle's radius.
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Acceleration is constantly changing.
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Acceleration points at right angles to V in the direction of the center of the circle.
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Positive acceleration points toward the center of the circle from the object.
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Negative acceleration points directly away from the center of the circle on the path of the circle-object.
- Centripetal Acceleration
- $$a_c = \frac{v^2}{r}$$
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- $$v$$ is the speed of motion.
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- $$r$$ is the radius of the circle.
- Circle Circumference
- $$2\pi r$$
- Area of a Circle
- $$\pi r^2$$
All forces can contribute to centripetal force. It's not a type of force, it's a function of an existing force.
- Centripetal Force
- $$F_c = \frac{mv^2}{r}$$
Circular Motion Problems
- Centripetal acceleration runs from object to the center of the circle.
- Multiple forces may contribute to the Centripetal Force.
- Forces pointing toward the center of the circle are positive.
- Forces pointing away from the center of the circle are negative.