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>
Answer:
Part a)

Part b)

Explanation:
As we know that torque is defined as the product of force and its perpendicular distance from reference point
so here we have

now we have


Part b)
Now we know the conversion as
1 meter = 3.28 foot
1 N = 0.225 Lb force
now we have



Answer:
0.243 m/s
Explanation:
From law of conservation of motion,
mu+m'u' = V(m+m')................. Equation 1
Where m = mass of the first car, m' = mass of the second car, initial velocity of the first car, u' = initial velocity of the second car, V = Final velocity of both cars.
make V the subject of the equation
V = (mu+m'u')/(m+m')................. Equation 2
Given: m = 260000 kg, u = 0.32 m/s, m' = 52500 kg, u' = -0.14 m/s
Substitute into equation 2
V = (260000×0.32+52500×(-0.14))/(260000+52500)
V = (83200-7350)/312500
V = 75850/312500
V = 0.243 m/s
Answer:
the third stage was 480 km long
Explanation:
Stage 1:
Time = 1 hours
Speed = 80km
Stage 2:
Time = 2 hours
Speed = 200km
Stage 3:
Time = 4 hours
Let the Distance at the stage 3 be x
Average speed of the train route = 100 km/h
So


Lets find the speed at stage 1
Speed = 
Speed = 
Speed 1= 80 km/hr
The speed at stage 2
Speed = 
Speed = 
Speed 2 = 100 km/hr
The speed at stage 3
Speed = 
Speed = 
Speed 3 = 
we kow that average is ,









x = 480
A decagram is 1000 times bigger than a centigram