[amp_mcq option1=”$$\\frac{{\\text{r}}}{{{{\\text{v}}^2}}}$$” option2=”$$\\frac{{{{\\text{v}}^2}}}{{\\text{r}}}$$” option3=”$$\\frac{{\\text{r}}}{{{\\omega ^2}}}$$” option4=”$$\\frac{{{\\omega ^2}}}{{\\text{r}}}$$ E. $${\\text{r}}\\omega $$” correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\frac{{{{\\text{v}}^2}}}{{\\text{r}}}}$.<\/p>\n
Centripetal acceleration is the acceleration of an object towards the center of a circle that it is moving in. It is always directed towards the center of the circle, and its magnitude is given by the formula:<\/p>\n
$$a_c = \\frac{v^2}{r}$$<\/p>\n
where $v$ is the linear velocity of the object and $r$ is the radius of the circle.<\/p>\n
Linear velocity is the rate at which an object changes its position. It is given by the formula:<\/p>\n
$$v = \\frac{ds}{dt}$$<\/p>\n
where $ds$ is the change in position and $dt$ is the change in time.<\/p>\n
Angular velocity is the rate at which an object rotates. It is given by the formula:<\/p>\n
$$\\omega = \\frac{d\\theta}{dt}$$<\/p>\n
where $\\theta$ is the angle through which the object rotates and $dt$ is the change in time.<\/p>\n
The relationship between linear velocity and angular velocity is given by the formula:<\/p>\n
$$v = r\\omega$$<\/p>\n
where $r$ is the radius of the circle.<\/p>\n
Substituting this into the formula for centripetal acceleration, we get:<\/p>\n
$$a_c = \\frac{(r\\omega)^2}{r} = \\omega^2$$<\/p>\n
Therefore, the centripetal acceleration of a moving body along the circular path of radius $r$ is $\\boxed{\\frac{{{{\\text{v}}^2}}}{{\\text{r}}}}$.<\/p>\n
The other options are incorrect because they do not take into account the radius of the circle.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”$$\\frac{{\\text{r}}}{{{{\\text{v}}^2}}}$$” option2=”$$\\frac{{{{\\text{v}}^2}}}{{\\text{r}}}$$” option3=”$$\\frac{{\\text{r}}}{{{\\omega ^2}}}$$” option4=”$$\\frac{{{\\omega ^2}}}{{\\text{r}}}$$ E. $${\\text{r}}\\omega $$” correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[645],"tags":[],"class_list":["post-6744","post","type-post","status-publish","format-standard","hentry","category-applied-mechanics-and-graphic-statics","no-featured-image-padding"],"yoast_head":"\n