![]() ![]() All the angular variables are related to the straight-line variables by a factor of r, the distance from the center of rotation to the point you're interested in.Īlthough points at different distances from the center of a rotating wheel have different velocities, they all have the same angular velocity, so they all go around the same number of revolutions per minute, and the same number of radians per second. (angle, for short) angular velocity, and angular acceleration. The equivalent variables for rotation are angular displacement Velocity, then, isn't the most convenient thing to use when you're dealing with rotation, and for the same reason neither is displacement, or acceleration it is often more convenient to use their rotational equivalents. If you spin a wheel, and look at how fast a point on the wheel is spinning, the answer depends on how far away the point is from the center. To solve rotational kinematics problems, a set of four equations is used these are essentially the one-dimensional motion equations in disguise. If you can do one-dimensional motion problems, which involve straight-line motion, then you should be able to do rotational motion problems, because a circle is just a straight line rolled up. We'll now switch the focus from straight-line motion to rotational motion. It may oscillate, but it won't fall over. Very large objects, large enough that the acceleration due to gravity varies in different parts of the object, are the only ones where the center of mass and center of gravity are in different places.įact 1 - An object thrown through the air may spin and rotate, but its center of gravity will follow a smooth parabolic path, just like a ball.įact 2 - If you tilt an object, it will fall over only when the center of gravity lies outside the supporting base of the object.įact 3 - If you suspend an object so that its center of gravity lies below the point of suspension, it will be stable. ![]() The center of mass of an object is generally the same as its center of gravity. In other words, for many purposes you can assume that object is a point with all its weight concentrated at one point, the center of gravity.įor any object, the x-position of the center of gravity can be found by considering the weights and x-positions of all the pieces making up the object:Ī similar equation would allow you to find the y position of the center of gravity. The center of gravity is an important point to know, because when you're solving problems involving large objects, or unusually-shaped objects, the weight can be considered to act at the center of gravity. Unless you've been exceedingly careful in balancing the object, the center of gravity will generally lie below the suspension point. If you suspend an object from any point, let it go and allow it to come to rest, the center of gravity will lie along a vertical line that passes through the point of suspension. The center of gravity of an object is the point you can suspend the object from without there being any rotation because of the force of gravity, no matter how the object is oriented. Center of gravity and Rotational variables
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