The sweet spot on a baseball bat is 120 cm from the axis of rotation during the swing of the bat. (This seems long at first, since the bat is shorter than 120 cm. But the bat’s axis of rotation is outside of the bat and passes through the body of the batter.) If the sweet spot on the bat moves 40 m/s, how fast is the angular velocity of the bat

Question

The sweet spot on a baseball bat is 120 cm from the axis of rotation during the swing of the bat. (This seems long at first, since the bat is shorter than 120 cm. But the bat’s axis of rotation is outside of the bat and passes through the body of the batter.) If the sweet spot on the bat moves 40 m/s, how fast is the angular velocity of the bat

Answer 1

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The angular velocity of the bat can be calculated using the equation: angular velocity = linear velocity/radius. In this case, the linear velocity is 40 m/s and the radius is 120 cm, so the angular velocity of the bat is 0.33 rad/s.

Answer 2

To find the angular velocity of the bat, we can use the formula:

Angular velocity = linear velocity / radius

Here, the linear velocity is given as 40 m/s and the distance of the sweet spot from the axis of rotation is given as 120 cm. Convert the sweet spot distance from centimeters to meters:

120 cm = 1.2 m

Now, we can substitute the values into the formula:

Angular velocity = 40 m/s / 1.2 m

Simplifying the equation, we get:

Angular velocity = 33.33 rad/s (rounded to two decimal places)

Therefore, the angular velocity of the bat is approximately 33.33 rad/s.

Answer 3

To determine the angular velocity of the bat, we need to know the distance from the axis of rotation to the sweet spot. In this case, the distance is given as 120 cm.

Angular velocity is defined as the rate at which an object rotates around an axis. It is typically measured in radians per second (rad/s).

To find the angular velocity, we can use the formula:

Angular velocity = Linear velocity / Radius

Now, we need to convert the given linear velocity of the sweet spot from meters per second (m/s) to centimeters per second (cm/s) because our radius is given in centimeters.

Given that the sweet spot moves at 40 m/s, we can convert it to cm/s using the fact that 1 m = 100 cm:

40 m/s = 40 * 100 cm/s = 4000 cm/s

Now, we can substitute the values into the formula:

Angular velocity = 4000 cm/s / 120 cm

Simplifying this equation gives us

Angular velocity = 33.33 rad/s

Therefore, the angular velocity of the bat is approximately 33.33 rad/s.