Question

baseball pitcher executes a pitch in 0.32 sec. (assume that his motion of the pitching arm is a circular, also assume that v₁ = 0). If his pitching arm is 90 cm long, what are the magnitudes of the tangential and radial accelerations on the ball just before ball release, when tangential ball speed is 35 m/s (in m/s²)? What is the magnitude of the total acceleration on the ball at this point (in m/s²)?

Answer 1

Initial speed of the ball = V₁ = 0 m/s

Final speed of the ball = V₂ = 35 m/s

Length of the pitching arm = L = 90 cm = 0.9 m

Initial angular speed of the ball = ₁ = V₁/L = 0/0.9 = 0 rad/s

Final angular speed of the ball = ₂ = V₂/L = 35/0.9 = 38.889 rad/s

Time period = T = 0.32 sec

Angular acceleration =

₂ = ₁ + T

38.889 = 0 + (0.32)

= 121.528 rad/s²

Radial acceleration of the ball just before the release = a_r

a_r = ₂²L

a_r = (38.889)²(0.9)

a_r = 1361.11 m/s²

Tangential acceleration of the ball just before the release = a_t

a_t = L

a_t = (121.528)(0.9)

a_t = 109.37 m/s²

Total acceleration of the ball = a

a = 1365.5 m/s²

a) Magnitude of tangential acceleration of the ball just before the release = 109.37 m/s²

b) Magnitude of radial acceleration of the ball just before the release = 1361.11 m/s²

c) Total acceleration of the ball just before the release = 1365.5 m/s²