Question

The cylinder rotates about the fixed z-axis in the direction indicated. If the speed of point A is v_A = 3.3 ft/sec and the magnitude of its acceleration is a_A = 50.6 ft/sec², determine the magnitudes of the angular velocity and angular acceleration of the cylinder. Is knowledge of the angle θ necessary?

y -- TO 4" А * Incorrect Find the magnitude of the angular acceleration of the disk. 235.34 Answer: a = rad/sec the tolerance is +/-2%

Answer 1

given

vA = 3.3 ft/s
aA = 50.6 ft/sec^2

r = 4''

= 4 inch

= 4/12 feet

= 1/3 feet

angular velocity, w = vA/r

= 3.3/(1/3)

= 9.9 rad/s <<<<<<----------Answer

radial acceleration, a_rad = v^2/r

= 3.3^2/(1/3)

= 32.67 ft/sec^2

let a_tan is the tangential acceleration.

a^2 = a_tan^2 + a_rad^2

50.6^2 = a_tan^2 + 32.67^2

==> a_tan = sqrt(50.6^2 - 32.67^2)

= 38.6 feet/sec^2

now use,

angular acceleration, alfa = a_tan/r

= 38.6/(1/3)

= 115.8 rad/s^2 <<<<<<<<<----------------Answer

knowledge of the angle theta is not necessary.