A disc of radius R is rotating with an angular speed ωo about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is µk.

(a) What was the velocity of its centre of mass before being brought in contact with the table?

(b) What happens to the linear velocity of a point on its rim when placed in contact with the table? (c) What happens to the linear speed of the centre of mass when disc is placed in contact with the table?

(d) Which force is responsible for the effects in (b) and (c).

(e) What condition should be satisfied for rolling to begin?

(f) Calculate the time taken for the rolling to begin.

This is a long answer type question as classified in NCERT Exemplar

(a) Before being bought in contact with the table the disc was in pure rotational motion. Hence V_cm=0

(b) when the disc is placed in contact with table due to friction centre of mass acquires some linear velocity.

(c) when the rotating disc is placed in contact with the table due to friction centre of mass acquires some linear velocity.

(d) friction is responsible for the effects ib b and c

(e) when rolling starts V_cm=wR

(f) time period for rolling to begin is t= $\frac{R{w}_o}{\mu g(1+\frac{m{R}^2}{I})}$

<p><span data-sheets-root="1">This is a long answer type question as classified in NCERT Exemplar</span></p><p><strong> (a)</strong> Before being bought in contact with the table the disc was in pure rotational motion. Hence V_cm=0</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745470641phpkbmNI3_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745470641phpkbmNI3.jpeg" alt="" width="195" height="118"></picture></div></div><p><strong> (b)</strong> when the disc is placed in contact with table due to friction centre of mass acquires some linear velocity.</p><p><strong> (c) </strong>when the rotating disc is placed in contact with the table due to friction centre of mass acquires some linear velocity.</p><p><strong> (d)</strong> friction is responsible for the effects ib b and c</p><p><strong> (e)</strong> when rolling starts V_cm=wR</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745470693phplSiwYW_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745470693phplSiwYW.jpeg" alt="" width="245" height="125"></picture></div></div><p><strong> (f)</strong> time period for rolling to begin is t=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>R</mi> <msub> <mrow> <mrow> <mi>w</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mi>μ</mi> <mi>g</mi> <mo> (</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mrow> <mi>m</mi> <msup> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mfrac> </math> </span></p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745470725phpQeeNgo_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745470725phpQeeNgo.jpeg" alt="" width="195" height="121"></picture></div></div>

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