Answer:
(a) the angular velocity at θ1 is 11.64 rad/s
(b) the angular acceleration is 0.12 rad/
(c) the angular position was the disk initially at rest is - 428.27 rad
Explanation:
Given information :
θ1 = 16 rad
θ2 = 76 rad
ω2 = 11 rad/s
t = 5.3 s
(a) The angular velocity at θ1
First, we use the angular motion equation for constant acceleration
Δθ = (ω1+ω2)t/2
θ2 - θ1 = (ω1+ω2)t/2
ω1 + ω2 = 2 (θ2 - θ1) / t
ω1 = (2 (θ2 - θ1) / t ) - ω2
= (2 (76-16) / 5.3) - 11
= 11.64 rad/s
(b) the angular acceleration
ω2 = ω1 + α t
α t = ω2 - ω1
α = (ω2 - ω1)/t
= (11.64 - 11) / 5.3
= 0.12 rad/
(c) the angular position was the disk initially at rest, θ0
at rest ω0 = 0
ω2^2 = ω01 t + 2 α Δθ
2 α Δθ = ω2^2
θ2 - θ0 = ω2^2 / 2 α
θ0 = θ2 - (ω2^2) / 2 α
= 76 - (
/ 2 x 0.12
= 76 - 504.16
= - 428.27 rad
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Complete Question
Q. Two go-carts, A and B, race each other around a 1.0km track. Go-cart A travels at a constant speed of 20m/s. Go-cart B accelerates uniformly from rest at a rate of 0.333m/s^2. Which go-cart wins the race and by how much time?
Answer:
Go-cart A is faster
Explanation:
From the question we are told that
The length of the track is 
The speed of A is 
The uniform acceleration of B is 
Generally the time taken by go-cart A is mathematically represented as
=> 
=> 
Generally from kinematic equation we can evaluate the time taken by go-cart B as
given that go-cart B starts from rest u = 0 m/s
So
=> 
=> 
Comparing 
we see that 
is smaller so go-cart A is faster
