Problem 2 The hammer throw is a track and field event where a 16 lb metal ball i

Question

Problem 2 The hammer throw is a track and field event where a 16 lb metal ball is attached to a wire (length 121.5 cm, blue arrow below). The thrower holds on to the wire with a handle and rotates around three to four times before releasing the hammer in an attempt to throw it as far as possible. A 5' 9" tall hammer throw athlete is assumed to be in the position shown below. Anthropometric data has shown that the extended grip reach (red arrow) of males is 46.6% of the person's total body height. If the tangential velocity of the ball is measured to be 25 m/s, what is the angular velocity of the ball? What is the angular velocity of the thrower's hands? What is the radial acceleration of the metal ball? If the thrower assumes to rotate at a constant rate, how many seconds would it take him to rotate through three complete revolutions?

Explanation / Answer

Here we have height = 5 ft 9 inch = 1.7526 m

Here extended grip = 0.466*1.7526 m

= 0.8167 m

Angular velocity = V/r

= 25/(0.8167+1.215)

= 12.3 rad/s answer

Angular velocity of his hand = 12.3 rad/s answer

Radial acceleration of ball = v^2 /r = 25^2 /(0.8167+1.215)

= 307.6 m/s^2 Answer

Time taken for 3 revolutions = 3*2pi/12.3

= 1.53 s answer

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