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27 Nov 2019
To find the velocity and acceleration vectors for uniform circularmotion and to recognize that this acceleration is the centripetalacceleration.
Suppose that a particle's position is given by the followingexpression:
\vec{r}(t)= R[\cos(\omega t)\hat{i} + \sin(\omega t)\hat{j}]
\,\ \qquad = R\cos(\omega t)\hat{i} + R\sin(\omega t)\hat{j}.
a) When does the particle first cross the negative x axis?
b)Find the particle's velocity as a function of time.
c)Find the speed of the particle at time t.
d)Now find the acceleration of the particle.
e)Your calculation is actually a derivation of the centripetalacceleration. To see this, express the acceleration of the particlein terms of its position r_vec(t).
To find the velocity and acceleration vectors for uniform circularmotion and to recognize that this acceleration is the centripetalacceleration.
Suppose that a particle's position is given by the followingexpression:
\vec{r}(t)= R[\cos(\omega t)\hat{i} + \sin(\omega t)\hat{j}]
\,\ \qquad = R\cos(\omega t)\hat{i} + R\sin(\omega t)\hat{j}.
a) When does the particle first cross the negative x axis?
b)Find the particle's velocity as a function of time.
c)Find the speed of the particle at time t.
d)Now find the acceleration of the particle.
e)Your calculation is actually a derivation of the centripetalacceleration. To see this, express the acceleration of the particlein terms of its position r_vec(t).
