A large stone disk is viewed from above and is initially at rest as seen in the

Question

A large stone disk is viewed from above and is initially at rest as seen in the figure below. The disk has a mass of 170.0 kg and a radius of 1.600 m. A constant force of 40.0 N is applied tangent to the edge of the disk for 59.0 s, causing the disk to spin around the z axis. Calculate the angular acceleration of the stone, finding both the direction and magnitude. (Express your answer in vector form. Substitute numeric values, do not use variables.) a rightarrow = rad/s^2 What is the final angular velocity of the stone? (Express your answer in vector form. Substitute numeric values, do not use variables.) omega rightarrow = rad/s Calculate the translational speed for a point on the edge of the stone after 59.0 s. = m/s

Explanation / Answer

a)
Moment of Inertia of the disk

I = (1/2)*M*R^2 = 0.5*170*1.6^2

= 217.6 kg.m^2

Torque, T = I*alfa

alfa = T/I = R*F*sin(90)/I = 1.6*40*1/217.6

= 0.294 rad/s^2

direction along +ve Z

b)

angular velocity w = wo + alfa*t = 0 +0.294*59

w = 17.35 rad/s

c)

speed v = R*w = 1.6*17.35

= 27.764 m/s

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