Answer:
The angular speed of the object is 0.0281 rad/s
The linear speed of the object is 0.169 ft/s
Explanation:
Given;
radius of the circle, r = 6 ft
time of motion of the object around the circle, t = 80 s
central angle formed by the object during the motion, θ = 9/4 rad = 2.25 rad
The angular speed of the object is calculated as;

The linear speed of the object is calculated as;
v = ωr
v = 0.0281 rad/s x 6ft
v = 0.169 ft/s
Answer:
0.8895m
Explanation:
Cable diameter = 0.0125m
Mass of elevator = 6450kg
Young Modulus(E) = 2.11*10¹¹N/m
∇l (change in length) =
L = 362m
A = Πr², but r = d / 2 = 0.0125 / 2 = 0.00625m
A = 3.142 * (0.00625)² = 1.227*10^-4m²
Young Modulus (E) = Tensile stress / Tensile strain
E = (F / A) / ∇l / L
F = mg = 6450 * 9.8 = 63210N
2.11*10¹¹ = (63210 / 1.22*10^-4) / (∇l / 362)
2.11*10¹¹ = 5.18*10⁸ / (∇l / 362)
2.11*10¹¹ = (5.18*10⁸ * 362) / ∇l
2.11*10¹¹ = 1.875*10¹¹ / ∇l
∇l = 1.875*10¹¹ / 2.11*10¹¹
∇l = 0.8895m
The change in length is 0.8895m
Answer:
A) and B) are correct.
Explanation:
Let's take a look at the attached picture. Now
The total voltage across both capacitors is the same as the sum of the voltage from each device, that statement is true for any electrical device connected in series. So a) is TRUE
The equivalent capacitance is going to be: 
And that value can be mathematically proven that is always less than any of the values of each capacitor. So b is TRUE
And through both capacitors flow the same current, but the amount of charge depends on the value of the capacitors, so only could be the same if the capacitors are the same value. Otherwise, don't. C) not always, so FALSE
Ahhh this going to be confusing sorry...
1. α = Δω / Δt = 28 rad/s / 19s = 1.47 rad/s²
2. Θ = ½αt² = ½ * 1.47rad/s² * (19s)² = 266 rads
3. I = ½mr² = ½ * 8.7kg * (0.33m)² = 0.47 kg·m²
4. ΔEk = ½Iω² = ½ * 0.47kg·m² * (28rad/s)² = 186 J
5. a = α r = 1.47rad/s² * 0.33m = 0.49 m/s²
6. a = ω² r = (14rad/s)² * 0.33m = 65 m/s²
7. v = ω r = 28rad/s * ½(0.33m) = 4.62 m/s
8. s = Θ r = 266 rads * 0.33m = 88 m