Answer:
16
Step-by-step explanation:
We are given that
Initial velocity,[tex]\omega_0[/tex]=0
Time=4 s
Number of revolutions in 4 s=4 rev=[tex]2\pi(4)rad[/tex]
Because 1 re=[tex]2\pi[/tex] rad
We have to find the number of revolutions made by wheel after 8 s.
[tex]\theta=\omega_0+\frac{1}{2}\alpha t^2[/tex]
Using the formula
[tex]2\pi(4)=0+\frac{1}{2}\alpha(4)^2[/tex]
[tex]\alpha=\pi[/tex]
Again, t=8
[tex]\theta=\frac{1}{2}(\pi)(8)^2=32\pi[/tex]
Number of rev=[tex]\frac{32\pi}{2\pi}=16[/tex]
To simplify question, the motion of a point on the wheel along a circular
path is assumed to be at a constant angular rate.
The number of revolution made by the wheel after 8 seconds is = 16
revolutions.
Reasons:
The given parameters are;
The motion of the wheel = Constant angular acceleration.
Number of revolutions made after four seconds = 4
Required:
The number of revolutions made after 8 seconds.
Solution:
The formula for finding the angle turned in an angular motion is similar to
the formula for finding the distance moved in linear motion.
For linear motion, we have;
s = u·t = (1/2)·a·t²
For an angular motion, we have;
θ = ω₀·t + (1/2)·α·t²
Where;
ω₀ = The given initial angular velocity = 0
α = angular acceleration
Therefore, for 4 revolutions, we have;
4×π×2 = 0 × 4 + (1/2) × α × 4² = 8·α
Therefore;
α = π
After 8 seconds, we have;
θ = 0 × 8 + (1/2) × π × 8² = 32·π
The angle turned after 8 seconds = 32·π
1 revolution = 2·π
Therefore;
[tex]Number \ of \ revolution \ made \ after \ 8 \ seconds = \dfrac{32 \cdot \pi}{2 \cdot \pi} = 16 \ revolutions[/tex]
The number of revolution made by the wheel after 8 seconds is = 16 revolutions.
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