If a body moves through a distance greater than 2 πR in one full rotation. Then: (a) vcm>R ω(b)

Name: Problem 39, Chapter 8: Arihant AIEEE Physics
Uploaded: 2021-09-25T00:58:43-08:00
Duration: 1 min 33 s
Channel: Dheeraj Sharma
Description: If a body moves through a distance greater than 2 πR in one full rotation. Then: (a) vcm>R ω(b) vcm R ω(d) vcm<R ω

step 1 In this question it is given that a body moves through a distance that is greater than 2 pi r in

Question

If a body moves through a distance greater than $2 \pi R$ in one full rotation. Then: (a) $v_{\mathrm{cm}}>R \omega$ (b) $v_{\mathrm{cm}}<R \omega$ (c) $v_{\mathrm{cm}}>R \omega$ (d) $v_{\mathrm{cm}}<R \omega$

   If a body moves through a distance greater than $2 \pi R$ in one full rotation. Then:
(a) $v_{\mathrm{cm}}>R \omega$
(b) $v_{\mathrm{cm}}<R \omega$
(c) $v_{\mathrm{cm}}>R \omega$
(d) $v_{\mathrm{cm}}<R \omega$

Arihant AIEEE Physics

D.B. Singh 2006 Edition

Chapter 8, Problem 39

Instant Answer

Solved by Expert Dheeraj Sharma

09/25/2021

Step 1

The angular velocity $\omega$ is then given by $\omega = \frac{2\pi}{T}$. Show more…

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If a body moves through a distance greater than $2 \pi R$ in one full rotation. Then: (a) $v_{\mathrm{cm}}>R \omega$ (b) $v_{\mathrm{cm}}<R \omega$ (c) $v_{\mathrm{cm}}>R \omega$ (d) $v_{\mathrm{cm}}<R \omega$

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Key Concepts

Rolling Motion

Rolling motion describes the combined rotational and translational movement of a body. In an ideal case of pure rolling without slipping, the point of contact with the surface is momentarily at rest, resulting in a fixed relationship where the linear speed (v_cm) equals the product of the angular speed (?) and the radius (R). This relationship implies that the distance covered in one complete rotation is exactly the circumference, 2?R.

Slipping in Rolling Motion

When the rolling body slips, it does not adhere to the no-slip condition, meaning that the point of contact with the surface is no longer momentarily at rest. This deviation results in a breakdown of the strict v_cm = R? relationship. If the distance traveled during one full rotation exceeds 2?R, it indicates that additional translation occurs due to slipping, making the center-of-mass linear speed greater than R?.

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