When a wheel moves a distance shorter than 2 πR while making one rotation, then: (a) vcm<R ω(b)

Name: Problem 38, Chapter 8: Arihant AIEEE Physics
Uploaded: 2021-09-25T00:56:22-08:00
Duration: 1 min 43 s
Channel: Dheeraj Sharma
Description: When a wheel moves a distance shorter than 2 πR while making one rotation, then: (a) vcm R ω(d) vcm>R ω

step 1 In this question it is given that when a wheel moves a distance shorter than 2 pi r while making

Question

When a wheel moves a distance shorter than $2 \pi R$ while making one rotation, then: (a) $v_{\mathrm{cm}}<R \omega$ (b) $v_{\mathrm{cm}}<R \omega$ (c) $v_{\mathrm{cm}}>R \omega$ (d) $v_{\mathrm{cm}}>R \omega$

   When a wheel moves a distance shorter than $2 \pi R$ while making one 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 38

Instant Answer

Solved by Expert Dheeraj Sharma

09/25/2021

Step 1

This means that the wheel is rolling without slipping. Show more…

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When a wheel moves a distance shorter than $2 \pi R$ while making one 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

Angular and Translational Velocity Relationship

The relationship between angular velocity (?) and translational velocity (v_cm) is a central concept in rotational dynamics. When an object rolls without slipping, the relation v_cm = R × ? holds true, where R is the radius. If the object rotates once but covers a distance less than the circumference (2?R), it implies that v_cm is less than R × ?, indicating that slipping or other factors are affecting the motion.

Rolling Without Slipping

Rolling without slipping is the ideal condition in which a rolling object's point of contact with the surface has zero velocity relative to that surface. This condition leads to a direct relationship between the object’s translational speed (the speed of its center of mass) and its angular velocity, such that the distance covered in one full rotation equals the circumference of the wheel. Deviations from this condition indicate that some form of slipping is occurring.

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