A wheel of radius R rolls on the ground with | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For a wheel rolling with a uniform velocity $v$ of its center of mass,the acceleration of the center of mass is $a_{CM} = 0$.Each point on the rim

Vedclass · Accepted Answer

$\frac{2v^2}{R}$

Vedclass · Answer

(B) For a wheel rolling with a uniform velocity $v$ of its center of mass,the acceleration of the center of mass is $a_{CM} = 0$.Each point on the rim of the wheel has a centripetal acceleration directed towards the center,given by $a_c = \frac{v^2}{R}$.Let the topmost point be $A$ and the bottommost point be $B$.The acceleration of point $A$ is $\vec{a}_A = \frac{v^2}{R}$ (directed downwards towards the center).The acceleration of point $B$ is $\vec{a}_B = \frac{v^2}{R}$ (directed upwards towards the center).The relative acceleration of $A$ with respect to $B$ is $\vec{a}_{AB} = \vec{a}_A - \vec{a}_B$.Taking the downward direction as positive,$\vec{a}_A = \frac{v^2}{R}$ and $\vec{a}_B = -\frac{v^2}{R}$.Thus,$\vec{a}_{AB} = \frac{v^2}{R} - (-\frac{v^2}{R}) = \frac{2v^2}{R}$.Therefore,the magnitude of the relative acceleration is $\frac{2v^2}{R}$.

$A$ wheel of radius $R$ rolls on the ground with a uniform velocity $v$. The relative acceleration of the topmost point of the wheel with respect to the bottommost point is

Similar Questions

$A$ hoop of radius $2 \; m$ weighs $100 \; kg$. It rolls along a horizontal floor so that its centre of mass has a speed of $20 \; cm/s$. How much work has to be done to stop it?

$A$ solid sphere is in rolling motion. In rolling motion,a body possesses translational kinetic energy $(K_t)$ as well as rotational kinetic energy $(K_r)$ simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is

$A$ round body is given a translational velocity and released on a surface that has friction. Then:

$A$ wheel of radius $2 \ cm$ is at rest on a horizontal surface. $A$ point $P$ on the circumference of the wheel is in contact with the horizontal surface. When the wheel rolls without slipping on the surface,the displacement of point $P$ after half a rotation of the wheel is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module