5. O 11 points M14 11.9.072 My Notes g is wrapped around a uniform disk of mass

Question

5. O 11 points M14 11.9.072 My Notes g is wrapped around a uniform disk of mass M 1.4 kg and radius R -0.11 m (see figure below). Attached to the disk are four low-mass rods of radius b - 0.13 m, each with a small mass m -0o.s kg at the end. The device is nitially at rest on a neaty frictionless surface. Then you pull the string with a constant force F 1 8 N for a time of 0.2 s. Now what is the angular speed of the apparatus? rad/s nm M.R Also calculate numerically the angle through which the apparatus turns, in radians and degrees rad Aedegrees Additional Materials Section 11.9

Explanation / Answer

Moment of inertia of assembly:
I = ½MR² + 4mb²
I = ½(1.4kg)(0.11m)² + 4(0.5kg)(0.13m)² = 0.04227 kg·m²

torque = I*
and also = F*R = 18N * 0.11m = 1.98 N·m
so
1.98 N·m = 0.04227 kg·m² *
= 46.84 rad/s²

= *t = 46.84rad/s² * 0.2s = 9.37 rad/s

(a) = ½t² = ½ * 46.84rad/s² * (0.2s)² = 0.94 radians  
(b) In degrees 53.86º

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