Question

1. A uniform disk with a 16 kg mass and a 20 cm radius rotates about a perpendicular axis through the center. Three forces act on it as shown. The 60 N and 50 N forces act at the rim with the 60 N tangent to it, and the 70 N acts at a distance of 10 cm from the axis as shown. (a) What is the net torque on the disk? (b) What is the angular acceleration of the disk? 3s LON

Answer 1

here,

1)

mass , m = 16 kg

radius , r = 0.2 m

a)

the net torque , T = 50 * cos(35) * r + 70 * 0.1 - 60 * sin(75 ) * r

T = 50 * cos(35) * 0.2 + 70 * 0.1 - 60 * sin(75 ) * 0.2

T = 3.6 N.m

the net torue is 3.6 N.m clockwise

b)

the angular accelration , alpha = net torque /moment of inertia

alpha = 3.6 /( 0.5 * m * r^2) = 3.6 /( 0.5 * 16 * 0.2^2) rad/s^2

alpha = 11.25 rad/s^2 clockwise