Respuesta :
The rotational velocity is expressed in [tex]{{{\text{rad}}} \mathord{\left/ {\vphantom {{{\text{rad}}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}[/tex] or [tex]{{\text{1}} \mathord{\left/ {\vphantom {{\text{1}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}[/tex] or [tex]{{\text{s}}^{{\text{ - 1}}}}[/tex].
Further Explanation:
The rotational velocity is the velocity of an object moving around a circular path or rotating or revolving relative to a point or axis of the object in a given interval of time. The rotational velocity is also known as the angular velocity.
Concept:
Consider an object, it starts to move on a circular path with a constant velocity [tex]v[/tex]. The distance between the center of the circular path and the object is fixed or constant throughout the motion, it is equal to the radius of the circular path i.e., [tex]r[/tex].
The object is initially, at rest, is placed at point [tex]A[/tex]. The object starts to move on the circular path and at time [tex]{t_1}[/tex] it reaches the point [tex]B[/tex] and makes an angle [tex]{\theta _1}[/tex] at the center of the circle with respect to its initial position i.e., point [tex]A[/tex]. At time [tex]{t_2}[/tex], the object makes an angle of [tex]{\theta _2}[/tex] at the center of the circle.
The angular velocity of an object moving on a circular path is defined as the ratio of change in angle made by the object at the center of the circular path with change in time.
The angular velocity is:
[tex]\fbox{\begin\omega= \dfrac{{{\theta _2} - {\theta _1}}}{{{t_2} - {t_1}}}= \dfrac{{\Delta \theta }}{{\Delta t}}\end{minispace}}[/tex] …… (1)
Here, [tex]\Delta \theta[/tex] is the change in the angle made by the object at the center of the circular path and [tex]\Delta t[/tex] is the change in time.
The angle, made by an object moving on a circular path, at the center of the circular path is measured in radians and time change in time or time interval is measured in seconds. Therefore, from equation (1), the unit of rotational velocity is [tex]{{{\text{rad}}} \mathord{\left/ {\vphantom {{{\text{rad}}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}[/tex].
The angular velocity is also defined as the ratio of linear velocity, with which the object is moving on circular path, and the distance between the center of the circular path and the object.
The angular velocity is:
[tex]\fbox{\begin\omega=\dfrac{v}{r}\end{minispace}}[/tex] …… (2)
The velocity of the object is measured in [tex]{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}[/tex] and the distance between the center of the circular path and the object is measured in [tex]{\text{m}}[/tex]. Therefore, the angular velocity or rotational velocity is measured in [tex]{{\text{1}} \mathord{\left/ {\vphantom {{\text{1}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}[/tex] or [tex]{{\text{s}}^{{\text{-1}}}}[/tex].
Thus, the rotational velocity is expressed in [tex]{{{\text{rad}}} \mathord{\left/ {\vphantom {{{\text{rad}}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}[/tex] or [tex]{{\text{1}} \mathord{\left/ {\vphantom {{\text{1}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}[/tex] or [tex]{{\text{s}}^{{\text{ - 1}}}}[/tex].
Learn more:
1. Acceleration of a moving object https://brainly.com/question/7031524
2. Change in momentum https://brainly.com/question/9484203
3. Conservation of energy https://brainly.com/question/3943029
Answer Details:
Grade: High School
Subject: Physics
Chapter: Kinematics
Keywords:
Angular velocity, rotational velocity, circular path, rotation, object revolving around a fixed point, change in the angle subtended at the center of circular path, radian/second, rad/sec, rad/s, 1/s, s^-1.
