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- https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/36%3A_Rotational_Motion/36.01%3A_Translational_vs._Rotational_MotionTaking derivatives of both sides with respect to time and using \(d s / d t=v\), \(d \theta / d t=\omega\), and \(r\) is constant, we get a relation between linear and angular velocities: Each of the ...Taking derivatives of both sides with respect to time and using \(d s / d t=v\), \(d \theta / d t=\omega\), and \(r\) is constant, we get a relation between linear and angular velocities: Each of the quantities we encountered in translational motion has a rotational counterpart, as shown in Table \(\PageIndex{1}\). (Time \(t\) is the same in both translational and rotational motion.)
- https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/36%3A_Rotational_MotionWe can describe the rotation of a solid body about an axis in a manner similar to the way we describe linear motion. First, instead of the giving position of the body along an axis, we specify its rot...We can describe the rotation of a solid body about an axis in a manner similar to the way we describe linear motion. First, instead of the giving position of the body along an axis, we specify its rotation angle \(\theta\) relative to an agreed-upon zero rotation angle. Then we define an angular velocity \(\omega\) in a way similar to the definition of linear velocity: We also define an angular acceleration \(\alpha\) that's analogous to linear acceleration:
- https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/35%3A_The_Cross_ProductMany of the equations involving rotational motion of bodies involve the vector cross product, so before proceeding further, let's examine the cross product of two vectors in some detail. In the cross ...Many of the equations involving rotational motion of bodies involve the vector cross product, so before proceeding further, let's examine the cross product of two vectors in some detail. In the cross product, one multiplies a vector by another vector, and gets another vector back as the result (unlike the dot product, which returns a scalar result). Unlike the other two kinds of vector multiplication, the cross product is only defined for three-dimensional vectors. \({ }^{1}\)
