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A track and field athlete is competing in the hammer throw event. The athlete is 181 cm tall with an arm length of 90 cm and is using a standard ball and chain for the event, which is 121 cm long. As the athlete begins to spin, their body becomes the center of the motion, with both arms holding onto the ball and chain handle.

If the initial linear velocity of the ball and chain is 29 m/s upon its release, how fast (total angular velocity in radians per second) was the athlete spinning it?

Answer :

Final answer:

The athlete was spinning the hammer at an angular velocity of approximately 23.97 radians per second using the linear velocity of 29 m/s and the length of the ball and chain as 1.21 meters.

Explanation:

To determine the total angular velocity of the hammer throw, we must first understand that the angular velocity (ω) can be calculated using the formula ω = v / r, where 'v' is the linear velocity and 'r' is the radius of the circular motion. In this case, the athlete's height and arm length are not directly relevant to calculating the angular velocity of the hammer throw, but the length of the ball and chain is crucial. Given that the ball and chain's length is 121 cm (or 1.21 m) and serves as the radius ('r') of the circular path, and the initial linear velocity ('v') is 29 m/s, we calculate the angular velocity as follows:

ω = v / r = 29 m/s / 1.21 m = 23.97 rad/s.

Therefore, the athlete was spinning the hammer at approximately 23.97 radians per second at the moment of its release.

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Rewritten by : Barada

The angular velocity is obtained from the calculation as 13.7 rad/s.

What is the angular velocity?

Let us recall that the term circular motion is applied to the kind of motion that is carried out by an object that is moving along a circular path. Given the fact that we have an object that is spinning around in a circular path, we can say that a circular motion is actually taking place in the system that involves the athlete, the ball and the rope.

We are told that the athlete is 181cm tall, with an arm length of 90 cm and is using a standard ball and chain for the event which is 121cm long. As the athlete begins to spin , their body becomes the center of the motion, with both arms holding on to the ball and chain handle then the initial linear velocity of the ball and chain is 29m/s upon its release.

We can now see that the radius of the path is 90 cm + 121 cm = 211cm or 2.11 m


Using;

V = rω

ω = V/r

ω = 29m/s/2.11 m

ω = 13.7 rad/s

Learn more about angular velocity:https://brainly.com/question/12446100

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