Answer to Question #117413 in Classical Mechanics for Mehmet Fazıl Kıymazaslan

Question

A uniform solid disk of mass M=10 kg and radius R=0.4 m is initially at rest. The disk can rotate freely about a fixed frictionless axle passing through the center of the disk and perpendicular to the disk. Two forces of magnitude F1=2 N and F2=1 N are applied tangentially to the disk, as shown in the figure below. The moment of inertia of a disk is given as I=½MR2.
(a) Calculate the magnitude of the nettorque dueto the two forces shown.
(b)Calculate the magnitude of the resulting angular acceleration.
(c) How long does it take the disk to complete one revolution?

Answer 1

a)

$$\tau=(2-1)(0.4)=0.4\ Nm$$

b)

$$\tau=I\alpha\to \tau=0.5mr^2\alpha\to 0.4=0.5(10)(0.4)^2\alpha$$

$$\alpha=0.5\frac{rad}{s^2}$$

c)

$$2\pi=\alpha T$$

$$T=12.6\ s$$