Shohei Ohtani pitches a fastball with a horizontal velocity of 40 m/s. The horizontal distance from the point of release to home plate is 17.50 m. Justin Turner, the Red Samurai, decides to swing the bat 0.30 s after the ball has been released by Ohtani. The average angular velocity of the bat is 12 rad/s. The angular displacement of the bat from the Red Samurai’s shoulder to hitting positions above the plate is between 1.5 and 1.8 rad.
Angular speed, acceleration and displacement
Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.
Angular Position
Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.
Shohei Ohtani pitches a fastball with a horizontal velocity of 40 m/s. The horizontal
distance from the point of release to home plate is 17.50 m. Justin Turner, the Red
Samurai, decides to swing the bat 0.30 s after the ball has been released by Ohtani. The
average
the Red Samurai’s shoulder to hitting positions above the plate is between 1.5 and 1.8
rad. A) Will the bat be in a hitting position above the plate when the ball is above the
plate? Assume the pitch is in the strike zone and that if Turner hits it, it’s a homerun
because the Dodgers are better than the Angels. B) Assume that Turner does hit the ball.
If the bat’s instantaneous velocity is 30 rad/s at the instant of contact, and the distance
from the sweet spot of the bat to the axis of rotation is 1.25 m, what is the instantaneous
linear velocity of the sweet spot at the instant of ball contact?
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