Physics Help Forum Dynamics of rotational motion problem

 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum

 Jun 20th 2017, 01:28 PM #1 Junior Member   Join Date: Jun 2017 Posts: 1 Dynamics of rotational motion problem Hello, I have this problem: A uniform solid cylinder with mass M and radius R has rolled up a string. The string runs through a pulley with negligible mass. a)Calculate the acceleration of mass m b)Discuss the conditions under which the cylinder slides while rotating could any one help me to solve this problem?
 Jun 21st 2017, 09:14 AM #2 Senior Member     Join Date: Aug 2008 Posts: 113 If those are solutions at the bottom of your diagram, then my calculations do not agree. Part (a) ... assuming no slippage by the cylinder on the horizontal surface $F_{net} = ma$ (1) $mg - T = ma$ (2) $T + f_s = Ma$ $\tau_{net} = I \alpha$ $TR - f_sR = \dfrac{1}{2}MR^2 \cdot \dfrac{a}{R}$ (3) $T - f_s = \dfrac{Ma}{2}$ sum equations (2) and (3) ... $2T = \dfrac{3Ma}{2} \implies T = \dfrac{3Ma}{4} \implies f_s = \dfrac{Ma}{4}$ substitute for $T$ in equation (1) ... $mg - \dfrac{3Ma}{4} = ma$ $4mg - 3Ma = 4ma \implies a = \dfrac{4mg}{3M+4m}$ Part (b) ... for no slippage, $f_s \le \mu Mg$. Slippage will occur when $\mu < \dfrac{f_s}{Mg}$ $\mu < \dfrac{1}{Mg} \cdot \dfrac{Ma}{4} = \dfrac{a}{4g} = \dfrac{1}{4g} \cdot \dfrac{4mg}{3M+4m} = \dfrac{m}{3M+4m}$ Attached Thumbnails   topsquark likes this.

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