The disk has an angular acceleration ?-9 rad/s2 and angular velocity w 2 rad/s a

Question

The disk has an angular acceleration ?-9 rad/s2 and angular velocity w 2 rad/s at the instant shown. It does not slip at A. (Figure 1) Part A Determine the magnitude of the acceleration of point B Express your answer to three significant figures and include the appropriate units IA aValue Units Submit Request Answer gure 1 of 1 Part B Determine the direction of the acceleration of point E. Express your answer using three significant figures 45° 0.5 m vec 54.7 o, measured clockwise from the negative r-axis

Explanation / Answer

A) we know,
a_tan = r*alfa

= 0.5*2

= 1 m/s^2

a_rad = r*w^2

= 0.5*2^2

= 2 m/s^2

total acceleration, a = sqrt(a_tan^2 + a_rad^2)

= sqrt(1^2 + 2^2)

= 2.24 m/s^2

B) ax = -a_rad*cos(45) + a_tan*cos(45)

= -2*cos(45) + 1*tan(45)

= -0.414 rad/s^2

ay = a_rad*sin(45) + a_tan*sin(45)

= 2*sin(45) + 1*sin(45)

= 2.12 rad/s^2

theta = tan^-1(ay/ax)

= tan^-1(2.12/0.414)

= 79.0 from -x axis in cclockwise direction.

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