The angle of a rotating shaft turns in t seconds is given by theta= ω+1/2at^2
and it is given that ω=3 2
rad/s and α=0.6 rad/s to complete θ=4 radians. Determine the time taken to complete θ=4 radians.
You posted these before as VINNY.
Perhaps if you labeled them as Physics, you might get a tutor to answer them.
btw, what does ω=3 2 mean? Is there a missing decimal ? , or ?
W= rad/s and a = 0.6. My mistake
Very sorry reiny it's just that I'm in desperate need of help and no one Is answering my questions. Could you please help me?
See previous post: Sat, 4-11-15, 4:23 AM.
To determine the time taken to complete θ=4 radians, we need to rearrange the formula theta=ωt+1/2at^2 and solve for t.
Given values:
ω = 3 rad/s (initial angular velocity)
α = 0.6 rad/s^2 (angular acceleration)
θ = 4 radians (angle to be completed)
Plug these values into the formula:
θ = ωt + (1/2)αt^2
Substituting the given values:
4 = 3t + (1/2)(0.6)t^2
Rearrange the equation to put it in standard quadratic form:
0.6t^2 + 3t - 4 = 0
Since this is a quadratic equation, we can solve it by factoring or using the quadratic formula. Let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from the equation:
a = 0.6, b = 3, c = -4
t = (-(3) ± √((3)^2 - 4(0.6)(-4))) / (2(0.6))
Simplifying the equation further:
t = (-3 ± √(9 + 9.6)) / 1.2
t = (-3 ± √18.6) / 1.2
Using a calculator, we can find the two possible answers:
t ≈ 1.45 seconds or t ≈ -5.12 seconds
Since time cannot be negative, the time taken to complete θ=4 radians is approximately 1.45 seconds.