Question

6. A sphere is moving towards (+ve) x-axis with a
velocity v, and rotates anticlockwise with angular
speed 'w' such that v. = wR/3
Speed of bottom
point of sphere is​

Answer 1

Answer:

$\bold{S_{B}=\frac{4 \omega R}{3}}$

Explanation:

From question, the sphere is moving in x-direction (positive) and anti-clockwise direction.

From this we can understand that the sphere is rolling. It is a combination of translational and rotational motion.

From question, the velocity of the sphere is:

$V_{c}=\frac{\omega R}{3}$

Now, the rotational speed is given as:

$S_{R}=\omega R$

Now, the translational speed is given as:

$S_{T}=\frac{\omega R}{3}$

Now, the speed at the bottom of the sphere is:

$\Rightarrow S_{B}=S_{R}+S_{T}$

$\Rightarrow S_{B}=\omega R+\frac{\omega R}{3}$

$\Rightarrow S_{B}=\frac{3 \omega R+\omega R}{3}$

$\therefore S_{B}=\frac{4 \omega R}{3}$