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 52 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

4.83rad/s and 14.50 rad/s

Explanation:

The distance from the center to the floor d = 52cm = 0.52m

Rotation is less than 1 rev

The toast rotates at a constant angular speed

Using kinematic d = Vit + 1/2gt^2

d = 0+1/2gt^2

t = (2d/g) square root

t = square root of 2× 0.52/ 9.8

t = 0.325s

The toast is accidentally pushed over the edge of the centre with butter side up, then the toast rotates as it falls . If the toast hits the ground and topples, the smallest angle will be less than 1/4 rev with correspondence to the smallest angular speed

Wmin = change in tetha/ change in time

= 0.25 rev/ change in t

= 0.25×2pii / change in t

= 0.5pii/0.325

= 0.5×3.142/0.325

= 4.83 rad/s

The toast is accidentally pushed over the edge of the centre with butter side up, then the toast rotates as it falls . If the toast hits the ground and topples, the maximum angle will be less than 3/4 rev with correspondence to the maximum angular speed

Wmax = change in tetha/ change in time

= 0.75 rev/ Change in time

= 0.75 ×2pii/change in tetha

= 1.5pii/0.325

= 1.5 ×3.142/0.325

= 14.50 rad/s

Note the following

Vi is the initial speed of the toast which is zero because it was initially at rest

t is the time taken for the toast to hit the floor

g is the gravitational acceleration

d is the distance between the counter and the floor. There is an attachment for you as well.

Thanks

not moving. pos accel,

we need to know the time interval during which the force acts. impulse of force = momentum change