cylindrical röller of mass m and radius r, initially stationary, is pulled along on a rough horizontal plane by a force F, as shown in the figure. a m i) Sketch the forces and torques acting on the roller. ii) By resolving forces horizontally and vertically show that the acceleration of the roller, a, will be given by: 2F a = Зт where u, is the coefficient of static friction. iii) Recalling that the condition for the roller to roll is that a = ar, where a is the angular acceleration of the cylinder, show that the cylinder will slide if: F> 3µsmg.

cylindrical röller of mass m and radius r, initially stationary, is pulled along on a rough horizontal plane by a force F, as shown in the figure. a m i) Sketch the forces and torques acting on the roller. ii) By resolving forces horizontally and vertically show that the acceleration of the roller, a, will be given by: 2F a = Зт where u, is the coefficient of static friction. iii) Recalling that the condition for the roller to roll is that a = ar, where a is the angular acceleration of the cylinder, show that the cylinder will slide if: F> 3µsmg.