Answer:
a) 4.49rad/s
b) 13.46rad/s
Explanation:
The distance from the counter to the floor =59m.
The toaster rotates at a constant speed less than 1 rev.
Using cinematic equation to calculate the time taken by the toast to hit the ground:
d = Vot + 1/2gt^2
59 = 0 + 1/2 × 9.81 × t^2
t = Sqrt(2 ×0. 59)/ 9.8)
t = Sqrt(1.18/9.8)
t = Sqrt(0.12041)
t =0. 347secs
As the toast is accidentally pushed over the counter with the side up, the toast rotates as it falls. If it hits the ground and topples to the butter side down, the smallest angle is 1/4 of A revolution.
W(min) = ΔΦ/Δt
W(min) = 0.25 rev/ 0.35
W(min) = 0.25 * 2π/0.35
W(min) = 1.57/0.35
W(min) = 4.49 rad/s
Same with the first part, the largest angle is 3/4 of a revolution
W(max) = ΔΦ/Δt
W(max) = 0.75 rev/0.35
W(max) = 0.75 * 2π/0.35
W(max) = 4.71/0.35
W(max) = 13.46 rad/s
Answer: a) 4.49 rad/s
b) 13.46 rad/s
Explanation:
distance from the counter to the floor, d = 59cm = 0.59m
Rotation is less than 1rpm
we use kinematics equation of motion to calculate the time taken by the toast to hit the floor
S = ut + 1/2at²
0.59 = 0 + 1/2*9.8*t²
1.18 = 9.8t²
t² = 1.18/9.8
t² = 0.12
t = 0.35s
As the toast is accidentally pushed over the counter with the side up, the toast rotates as it falls. If it hits the ground and topples to the butter side down, the smallest angle is 1/4 of A revolution.
W(min) = ΔΦ/Δt
W(min) = 0.25 rev/ 0.35
W(min) = 0.25 * 2π/0.35
W(min) = 1.57/0.35
W(min) = 4.49 rad/s
Same with the first part, the largest angle is 3/4 of a revolution
W(max) = ΔΦ/Δt
W(max) = 0.75 rev/0.35
W(max) = 0.75 * 2π/0.35
W(max) = 4.71/0.35
W(max) = 13.46 rad/s
