Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsRotational Dynamics4 Marks
Question
Define and explain centripetal force.
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Answer
Definition : In the uniform circular motion of a particle, the centripetal force is the force on the particle which at every instant points radially towards the centre of the circle and produces the centripetal acceleration to move the particle in its circular path. Explanation : A uniform circular motion is an accelerated motion, with a radially inward (i.e., centripetal) acceleration $-\frac{v^2}{r} \hat{\mathbf{r}}$ or $-\frac{v^2}{r} \hat{\mathbf{r}}$, where $\vec{r}$ is the radius vector and $\hat{\mathbf{r}}$ is a unit vector in the direction of $\vec{r}$. Hence, a net real force must act on the particle to produce this acceleration. This force, which at every instant must point radially towards the centre of the circle, is called the centripetal force. If $m$ is the mass of the particle, the centripetal force is $-\frac{m v^2}{r} \hat{\mathrm{r}}$ or $-m \omega^2 \vec{r}$. Notes : 1. As viewed from an inertial frame of reference, the centripetal force is necessary and sufficient for the particle to perform UCM. At any instant, if the centripetal force suddenly vanishes, the particle would fly off in the direction of its linear velocity at that instant. 2. In case the angular or linear speed changes with time, as in nonuniform circular motion, the force is not purely centripetal but has a tangential component which accounts for the tangential acceleration.
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