A uniform solid disk of mass 2.0 kg and radius 0.15 m is free to rotate about a…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A uniform solid disk of mass 2.0 kg and radius 0.15 m is free to rotate about a frictionless axle through its center. Three light cords are wrapped around the rim and exert the following constant forces in the plane of the disk:
• Cord A exerts a 6.0 N pull tangent to the rim, directed to increase the disk’s angular velocity counter-clockwise.
• Cord B exerts a 4.0 N pull tangent to the rim, directed to increase the angular velocity clockwise.
• Cord C is attached at a point on the rim where the tangent makes an angle of 60° above the horizontal. The cord is pulled with a 5.0 N force directed horizontally to the right.
Assume the disk is initially at rest at t = 0.
(a) For each cord, state whether the torque it produces about the axle is positive (counter-clockwise), negative (clockwise), or zero. Justify your answers without performing explicit calculations of torque magnitude.
(b) Determine the net torque acting on the disk. Express your answer in N·m, taking counter-clockwise to be the positive direction.
(c) Rank the three individual torques by the magnitude of the angular acceleration each would produce if it acted alone on the disk, from greatest to least. Clearly explain your reasoning.
(d) Using your result from part (b), determine the magnitude and direction of the disk’s angular acceleration at t = 0.