Item 9 A uniform disk with mass 36.5 kg and radius 0.270 m is pivoted at its cen

Question

Item 9 A uniform disk with mass 36.5 kg and radius 0.270 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 30.5 N is applied tangent to the rim of the disk. Part A What is the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.160 revolution? Express your answer with the appropriate units. Part B What is the magnitude a of the resultant acceleration of a point on the rim of the disk after the disk has turned through 0.160 revolution? Express your answer with the appropriate units. Item 10 In the figure the lower disk, of mass 420 g and radius 3.0 cm , is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 280 g and radius 2.2 cm , is initially not rotating. It drops freely down onto the lower disk, and frictional forces bring the two disks to a common rotational speed. (Figure 1) Part A Find the final common frequency in rpm. Express your answer using two significant figures. Part B Find the percentage of the initial kinetic energy lost to friction. Express your answer using two significant figures.

Explanation / Answer

the moment of inertia of a soid disk is = 0.5* M * R^2

the torque is F x R since the force is applied tangentially to the rim of the disk, so we have

F * R = 0.5 * M * R^2 alpha

alpha = 2 F/M R = 2 * 30.5N / (36.5 kg * 0.27m) = 6.2 rad/s/s

0.16 rev = 1 rad

find angular velocity from

wf^2 = w0^2 + 2 alpha theta

wf, w0 = final, initial ang vel
alpha = ang accel = 6.2 rad/s/s
theta = angular displacement = 1 rad

wf^2 = 0 + 2 * 6.2 * 1 => wf = 3.52 rad/s

this is the angular velocity, the linear velocity = w r = 0.95 m/s

b)

resultant accel = sqrt[a centip^2 + a tangential^2]

the linear acceleration = alpha r = 6.2 rad/s/s x 0.27m = 1.674 m/s^2

a centrip = v^2/r = 0.95^2 / 0.27 = 3.34 m/s2

resulstnat accel = sqrt( 3.34^2 + 1.674^2)

= 3.73 m/s^2

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