In the game of baseball, a pitcher throws a curve ball with as much spin as possible. This spin makes the ball “curve” on its way to the batter. In a typical case, the ball spins at about 20.5 revolutions per minute. What is the maximum centripetal acceleration of a point on the edge of the baseball? Assume the diameter of the baseball is approximately 10 cm.

Question

In the game of baseball, a pitcher throws a curve ball with as much spin as possible. This spin makes the ball “curve” on its way to the batter. In a typical case, the ball spins at about 20.5 revolutions per minute. What is the maximum centripetal acceleration of a point on the edge of the baseball? Assume the diameter of the baseball is approximately 10 cm.

Answer 1

centripetal acceleration = R*w^2

R = 5.0 cm
w is the angular velocity in radians/sec

20.5 rpm = 2.15 rad/s

That would not be much of a curve ball. 20.5 rpm is rather slow rotation and practically a knuckle ball.

Answer 2

The curve ball spin rate you were given is way off. It is typically over 20 revolutions per SECOND.

See

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Answer 3

To find the maximum centripetal acceleration of a point on the edge of the baseball, we can use the formula for centripetal acceleration:

a = (v^2) / r

Where:
a = centripetal acceleration
v = linear velocity
r = radius

In this case, we need to find the linear velocity of the point on the edge of the baseball and use the given information about the spin rate.

First, we need to convert the spin rate of 20.5 revolutions per minute to radians per second. Since there are 2π radians in one revolution and 60 seconds in one minute, we can use the following conversion factor:

20.5 revolutions/minute * 2π radians/revolution * 1/60 minutes/second = 20.5 * 2π / 60 radians/second

Now, let's find the linear velocity of the point on the edge of the baseball. The linear velocity of a point on the edge of a rotating object can be calculated by multiplying the angular velocity (spin rate) by the radius:

v = ω * r

Where:
v = linear velocity
ω = angular velocity (in radians per second)
r = radius

Given the diameter of the baseball is approximately 10 cm, we can calculate the radius:

radius = diameter / 2 = 10 cm / 2 = 5 cm

Now, let's substitute the given values into the formula to find the linear velocity:

v = (20.5 * 2π / 60) * 5 cm

Simplifying the expression:

v ≈ 10.77 cm/s

Now, we have the linear velocity. Let's substitute this value along with the radius into the formula for centripetal acceleration:

a = (v^2) / r

a = (10.77 cm/s)^2 / 5 cm

Simplifying the expression:

a ≈ 23.08 cm/s^2

Therefore, the maximum centripetal acceleration of a point on the edge of the baseball is approximately 23.08 cm/s^2.