Answer:
The angular acceleration of the pencil<em> α = 17 rad·s⁻²</em>
Explanation:
Using Newton's second angular law or torque to find angular acceleration, we get the following expressions:
τ = I α (1)
W r = I α (2)
The weight is that the pencil has is,
sin 10 = r / (L/2)
r = L/2(sin(10))
The shape of the pencil can be approximated to be a cylinder that rotates on one end and therefore its moment of inertia will be:
I = 1/3 M L²
Thus,
mg(L / 2)sin(10) = (1/3 m L²)(α)
α(f) = 3/2(g) / Lsin(10)
α = 3/2(9.8) / 0.150sin(10)
<em> α = 17 rad·s⁻²</em>
Therefore, the angular acceleration of the pencil<em> </em>is<em> 17 rad·s⁻²</em>
Complete Question
The complete question is shown on the first uploaded image
Answer:
The velocity is
in positive x -direction
The speed is 
Explanation:
From the question we are told that
The distance from the house to truck is D = 20 m
The distance traveled back to retrieve wind-blown hat is d = 15
The distance from the wind-blown hat position too the truck is k = 20 m
The total time taken is t = 75 s
Generally when calculating the displacement the Justin's backward movement to collect his wind - blown hat is taken as negative
Generally Justin's displacement is mathematically represented as

=> 
Generally the average velocity is mathematically represented as

=> 
=>
Generally the distance covered by Justin is mathematically represented as

=> 
=> 
Generally Justin's average speed over a 75 s period is mathematically represented as

=> 
=> 
Answer:
a) L = 3.29 10⁻⁴ H, b)U = 5.33 10⁻² J
Explanation:
a) The inductance is a solenoid this given carrier
L =
The magnetic field inside the solenoid is
B = μ₀
hence the magnetic flux
Ф_B = B. A = μ₀
we substitute in the expression of inductance
L = N² μ₀ A /l
let's find the area of each turn
A = π r²
A = π 0.02²
A = 1.2566 10⁻³ m²
let's calculate
L = 250² 4π 10⁻⁷ 1.2566 10⁻² / 0.3
L = 3.29 10⁻⁴ H
b) The stored energy is
U = ½ L i²
let's calculate
U = ½ 3.29 10⁻⁴ 18²
U = 5.33 10⁻² J
The horizontal force needed to start the calculator moving from rest is 1.5 N
What is Kinetic friction?
It is defined as a force that acts between moving surfaces.
The magnitude of the force will depend on the coefficient of kinetic friction between the two materials.
Here,
weight of calculator, N = 3 N
The coefficients of static frictions, µ (static) = 0.50
The coefficients of kinetic frictions, µ (kinetic) = 0.40
Now,
The horizontal force required = The static friction force
F = µ (static) * weight of calculator
F = 0.50 * 3.0
F = 1.5 N
Hence,
The horizontal force needed to start the calculator moving from rest is 1.5 N
Learn more about horizontal force here:
<u>brainly.com/question/21481680</u>
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