The starting angle θθ of a pendulum does not affect its period for θ<<1θ<<1. At higher angles, however, the period TT increases with increasing θθ.
The relation between TT and θθ can be derived by solving the equation of motion of the simple pendulum (from F=ma)
−gsinθ=lθ¨−gainθ=lθ¨
For small angles, θ≪1,θ≪1, and hence sinθ≈θsinθ≈θ. Hence,
θ¨=−glθθ¨=−glθ
This second-order differential equation can be solved to get θ=θ0cos(ωt),ω=gl−−√θ=θ0cos(ωt),ω=gl. The period is thus T=2πω=2πlg−−√T=2πω=2πlg, which is independent of the starting angle θ0θ0.
For large angles, however, the above derivation is invalid. Without going into the derivation, the general expression of the period is T=2πlg−−√(1+θ2016+...)T=2πlg(1+θ0216+...). At large angles, the θ2016θ0216 term starts to grow big and cause
As the speed of airplane is change due to jet stream
So the net speed is given as
now we can rearrange it as
now by the formula of vector difference we have
now plug in all values
so above is the speed of the plane
<span>The athlete is sweating, straining, sweating, trembling and groaning.
But if he passed high school physics, then he may remember that
'work' in physics means (force) x (distance). If there's no distance,
then there's no work.
He realizes that he isn’t doing any work because he's not moving the weight.</span>
The material that is the best choice for the head of a hammer is a metal. Having a metal for a hammer head allows you to have a light-weight but heavy duty hammer. Since a hammer is a tool that is used to strike an object repeatedly, a light weight is essential since you would be repeatedly making that motion.