When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor is 62 cm and for rotation less than 1 rev, what are the (a) smallest and (b) largest angular speeds that cause the toast to hit and then topple to be butter-side down? Assume free-fall acceleration to be equal to 9.81 m/s2.

The smallest angular velocity is 4.42 rad/s and the largest angular velocity is 13.15 rad/s for the toast to hit and then topple to be butter-side down

Explanation:

62 cm = 0.62 m

Knowing that the vertical distance traveled is s = 0.62 m and gravitational acceleration is g = 9.81 m/s2, we can calculate the time of falling

If there's only 0.36s to rotate, and for the toast to hit and then topple to be butter-side down, then the angle of rotation must be between 90 and 270 degrees (Suppose that it starts with butter up and it rotates less than 1 revolution, or 360 degrees):

In other words (and units):

rad

As :

rad/s

rad/s

rad/s

So the smallest angular velocity is 4.42 rad/s and the largest angular velocity is 13.15 rad/s for the toast to hit and then topple to be butter-side down