Question

(1) A good baseball pitcher can throw a baseball toward home plate at 93 mi/h with a spin of 1200 rev/min. How many revolutions does the baseball make on its way to home plate? For simplicity, assume that the 60 ft trajectory is a straight line.

(2) When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. Suppose the distance to the floor is 98 cm and the toast rotates less than 1 rev.

(a) What is the smallest angular speed that causes the toast to hit and then topple to be butter-side down?

(b) What is the largest angular speed that causes the toast to hit and then topple to be butter-side down?

Answer 1

2) Answer:

First find out how long it takes to fall from the equation s = 0.5gt²:

t = sqrt[2s/g]

where s is the fall distance (0.98m)

Assume the butter side is up on the table. For it to fall butter side down, it has to rotate at least 90º (p/2) before hitting the floor. It will land on an edge and momentum will carry it over. For it to fall butter side up it has to rotate more than 270º (3p/2) landing on the other edge.

a) The smallest angular speed is (p/2)/v[2s/g] rad/sec.

b) The fastest angular speed is (3p/2)/[2*s/g] rad/sec