A discus thrower (with arm length of 1.02 m) starts from rest and begins to rota

Question

A discus thrower (with arm length of 1.02 m) starts from rest and begins to rotate counterclockwise with an angular acceleration 2.91 rad/s^2. How long does it take the discuss thrower's speed to get to 4.47 rad/s? Tries 1/5 How many revolutions does the thrower make to reach the speed of 4.47 rad/s? Tries 0/5 What is the linear speed of the discus at 4.47 rad/s? Tries 0/5 What is the linear acceleration of the discus thrower at this point? Tries 0/5 What is the magnitude of the centripetal acceleration of the discus thrown? Tries 0/5 What is the magnitude of the discus' total acceleration? Tries 1/5

Explanation / Answer

(A) alpha = 2.91 rad/s^2

w = w0 + alpha t

4.47= 0 + 2.91 t

t = 1.54 sec .........Ans

(b) wf^2 - w0^2 = 2 alpha theta

4.47^2 - 0^2 = 2 (2.91) (theta)

theta = 3.43 rad

revolutions = 3.43 / 2pi = 0.55 revolutions

(c) v= w r = 4.47 x 1.02 = 4.56 m/s

(d) a_t =alpha r = 2.97 m/s^2

(e) a_c = w^2 r = 20.38 m/s^2

(f) magnitude of total acc. = sqrt(a_t^2 + a_c^2 ) = 20.60 m/s^2

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