An athlete spins in a circle before releasing a discus with a tangential speed of 9.0 m/s. If his angular speed at the moment of release was 12.0 rad/s, how far was the discus from his axis of rotation?
To find the distance of the discus from the athlete's axis of rotation, we need to use the formula for tangential speed:
Tangential speed = Angular speed * Radius
In this case, we know the tangential speed (9.0 m/s) and the angular speed (12.0 rad/s). We want to find the radius.
Rearranging the formula, we get:
Radius = Tangential speed / Angular speed
Substituting the known values:
Radius = 9.0 m/s / 12.0 rad/s
Calculating:
Radius = 0.75 m
Therefore, the discus was 0.75 meters away from the athlete's axis of rotation.
To find the distance of the discus from the athlete's axis of rotation, we can use the formula:
Distance = Speed / Angular Speed
Given:
Tangential Speed (v) = 9.0 m/s
Angular Speed (w) = 12.0 rad/s
Substituting the values into the formula, we get:
Distance = 9.0 m/s / 12.0 rad/s
Simplifying the expression, we have:
Distance = 0.75 m
Therefore, the discus was 0.75 meters away from the athlete's axis of rotation.