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 76 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

a.3.99rad/s

b.11.9604rad/s

Explanation:

Let, be distance from the counter to the floor and rotation of less than 1rev. is the time it takes to hit the floor.

#The toast rotates at a constant angular speed as it falls, with a constant gravitational acceleration.

#Using Kinematic equations:

#The lands on one of the edges if it topples to be butter-side down. Thus the smallest angle is 0.25rev which corresponds to the smallest angular velocity.

Hence, the smallest angular speed is 3.99rad/s

b. #The lands on one of the edges if it topples to be butter-side down. Thus the smallest angle is 0.75rev which corresponds to the largest angular velocity.

Hence, the largest angular speed is 11.9604rad/s

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