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 1.2 rad/s2. (a) How long does it take the discus thrower's speed to get to 1.9 rad/s? (b) How many revolutions does the thrower make to reach the speed of 1.9 rad/s? revolutions (c) What is the linear speed of the discus at 1.9 rad/s? (d) What is the tangential acceleration of the discus thrower at this point? (e) What is the magnitude of the centripetal acceleration of the discus thrown? (f) What is the magnitude of the discus's total acceleration?

Explanation / Answer

If a = angular acceleration, and ? = angular velocity, then for constant a ? = a*t the total angle is ? = 0.5*a*t² For (a) find t from the first equation and use it in the second: ? = 0.5*?²/a Linear (tangential) speed is r*? Tangential acceleration is r*a Centripetal acceleration is r*?² The total acceleration magnitude a = v[(tang acc)² + (centr acc)²] a =r*v[a² + ?^4] The angle is arctan[(centr acc)/(tang acc)] = arctan[?²/a]

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