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System of Particles and Rotational Motion

Rolling motion

A heavy homogeneous cylinder has mass m and radius R. It is ac

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A heavy homogeneous cylinder has mass $m$ and radius $R$ . It is accelerated by a force $F$ , which is applied through a rope wound around a light drum of radius $r$ attached to the cylinder (figure). The coefficient of static friction is sufficient for the cylinder to roll without slipping. (a) Find the friction force. (b) Find the acceleration $a$ of the centre of the cylinder. (c) Is it possible to choose $r$ , so that $a$ is greater than $\frac{F}{m}$ ? How? (d) What is the direction of the friction force in the circumstances of part (c)?

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Book:

Mechanics Volume 2 (DC Pandey)

Text solutionVerified

a = R α or \frac{F - f}{m} = R [\frac{F r + f R}{\frac{1}{2} m R ^{2}}]

Solving this equation, we get

f = \frac{2}{3} (\frac{1}{2} - \frac{r}{R}) F

(b) Acceleration

a = \frac{F - f}{m}

Substituting value of

f

from part (a), we get

a = \frac{2 F}{3 m R} (R + r)

(c)

a > \frac{F}{m}

\frac{2}{3 R} (R + r) > 1

r > \frac{R}{2}

(d) In this case force of friction is in forward direction.

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Mateo Discussed

A heavy homogeneous cylinder has mass

m

and radius

R

. It is accelerated by a force

F

, which is applied through a rope wound around a light drum of radius

r

attached to the cylinder (figure). The coefficient of static friction is sufficient for the cylinder to roll without slipping. (a) Find the friction force. (b) Find the acceleration

a

of the centre of the cylinder. (c) Is it possible to choose

r

, so that

a

is greater than

\frac{F}{m}

? How? (d) What is the direction of the friction force in the circumstances of part (c)?

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Question Text	A heavy homogeneous cylinder has mass $m$ and radius $R$ . It is accelerated by a force $F$ , which is applied through a rope wound around a light drum of radius $r$ attached to the cylinder (figure). The coefficient of static friction is sufficient for the cylinder to roll without slipping. (a) Find the friction force. (b) Find the acceleration $a$ of the centre of the cylinder. (c) Is it possible to choose $r$ , so that $a$ is greater than $\frac{F}{m}$ ? How? (d) What is the direction of the friction force in the circumstances of part (c)?
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	78

Text solutionVerified

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