Homework 10 Paper - Due Wed. April 6 - 5:00 pm Rotation, Torque, Energy and Angu

Question

Homework 10 Paper - Due Wed. April 6 - 5:00 pm Rotation, Torque, Energy and Angular Momentum Problem 1: Shown below is a solid disc of mass 100 g (M = 100 g), and radius of 10 cm (R= 10 cm) and moment of inertia about its center of mass equal to I_com = 1/2MR^2. The disc is initially rotating at 10 revolutions per second into the page as shown in the top view of the figure. A constant force of 10 N is being applied always tangent to the disc a distance of 2R away from the axis of rotation. Answer the following questions in regards to the configuration. Do not consider any friction or forces due to gravity in this problem. The top view will be the reference for all directions in this problem rotational variable directions will be into the page or out of the page. Calculate the magnitude and direction of the initial angular velocity Calculate the magnitude and direction of the torque acting on the disc Calculate the moment of inertia about the rotation axis Calculate the angular acceleration of the disc Calculate the magnitude and direction of the discs angular velocity after 1 second Calculate the rotational kinetic energy of the disc after 1 second Calculate the angular momentum of the disc after 1 second Graph theta, mu, alpha vs. time

Explanation / Answer

angular velocity w = 10*2*pi rad/s on = 62.83 rad/s

direction clockwise

(b)

torque = 2R*F = 2*0.1*10 = 2 Nm

direction counter clockwise

(c)

I = (1/2)*M*R^2 + M*R^2

I = (3/2)*M*R^2 = (3/2)*0.1*0.1^2 = 0.0015 kg m^2

(d)

torque = I*alpha

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2 = 0.0015*alpha

alpha = 1333.33 rad/s^2

(e)

alpha = (w2-w1)/t

1333.33 = (w2-62.83)/1

w2 = 1396 rad/s

f)

KE = 0.5*I*w2^2

KE = 0.5*0.0015*1396^2

KE = 1461.612 J

g)L = I*w2 = 0.0015*1396 = 2.094 kg m^2 /s

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