Question

Baseball pitching machines such as shown in (Figure 1) are used to fire baseballs toward a batter for hitting practice. In one kind of machine, the ball is fed between two wheels that are rapidly rotating in opposite directions; as the ball is pulled in between the wheels, it rapidly accelerates up to the speed of the wheels' rims, at which point it is ejected.

For a machine with 35-cm-diameter wheels, what rotational frequency (in rpm) do the wheels need to pitch a 85 mph fastball?

Express your answer in revolutions per minute.

f=_____rpm

Answer 1

1 mile = 1609.344 meter

1 hour = 3600 seconds

1 revolution = 2 radians

1 minute = 60 seconds

Diameter of the wheels = D = 35 cm = 0.35 m

Radius of the wheels = R = D/2 = 0.35/2 = 0.175 m

Speed the baseball is pitched at = V = 85 mph = 85 x (1609.344/3600) m/s = 38 m/s

Angular speed of the wheel =

The baseball reaches the same speed as the point on the rim of the wheel.

= 217.14 rad/s

Rotational frequency of the wheels (in rpm) = f

f = 2073.5 rpm

Rotational frequency of the wheels = 2073.5 rpm