A discus thrower (with arm length of 1.2 m) starts from rest and begins to rotat

Question

A discus thrower (with arm length of 1.2 m) starts from rest and begins to rotate counterclockwise with an angular acceleration of 2.3 rad/s^2. How long does it take the discuss thrower's speed to get to 3.2 rad/s^2? How many revolutions does the thrower make to reach the speed of 3.2 rad/s? revolutions What is the linear speed of the discus at 3.2 rad/s? What is the tangential acceleration of the discus thrower at this point? What is the magnitude of the centripetal acceleration of the discus thrown? what is the magnitude of the discus's toatal acceleration?

Explanation / Answer

w1 = 0

alfa = 2.3 rad/s^2

a) w2 = 3.2 rad/s

Apply, w2 = w1 + alfa*t

==> t = (w2 - w1)/alfa

= (3.2 - 0 )/2.3

= 1.39 s

b) theta = (w2^2 - w1^2)/(2*alfa)

= (3.2^2 - 0^2)/(2*2.3)

= 2.226 rad

= 2.226/(2*pi) rev

= 0.3544 revolutions

c) v = r*w2

= 1.2*3.2

= 1.2*3.2

= 3.84 m/s

d) a_tan = r*alfa

= 1.2*2.3

= 2.76 m/s^2

e) a_rad = r*w2^2

= 1.2*3.2^2

= 12.29 m/s^2

f) a_total = sqrt(a_tan^2 + a_rad^2)

= sqrt(2.76^2 + 12.29^2)

= 12.6 m/s^2

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