Question

A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), its velocity with respect to the road is: A) 2v. B) zero. C) 1.5v. D) v. E) The velocity depends on the radius of the tire.

Answer 1

Answer:

2V.

Explanation:

We know rolling motion is superposition of rotational and translational motion.

Also, it is rolling without slipping.

Therefore, $V=\omega \times R$       .....1

Where, V is linear velocity and $\omega$ is angular velocity of tire.

Now, at the top point :

Its, linear velocity is V because the tire it is moving with a velocity V.

Now , it is at a distance R from the center of tire.

Its , Velocity due to rotation $V_r=\omega \times R$.  {because is is not slipping}.

Both these velocities are in same direction.

Therefore, $V_t=V+V_r\\V_t=V+V=2V$

Because, $V_r=V$         ( from 1)

Hence, it is the required solution.

Answer 2

Answer:

The correct answer is option 'a': 2v

Explanation:

For a object under pure rolling the velocity of any point is given by

$v_{rolling}=v_{translational}+v_{rotational}$

Since in case of pure rolling the angular velocity is related to the transnational velocity as

$\omega =\frac{v_{translational}}{r}$

positive value is taken as the velocities have the same direction.

Thus the rotational velocity is given by

$v_{rotational}=\omega \times r\\\\\\v_{rotational}=\frac{V_{trans}}{r}\times r\\\\v_{rotational}=v_{trans}$

Thus the velocity at the tip becomes

$v_{rolling}=v+v\\\\v_{rolling}=2v$