Uniform Circular Motion:

Question

Suppose that a particle's position is given by the following expression:

r(t) = Rcos(omega*t)i + Rsin(omega*t)j

1. Choose the answer that best completes the following sentence:
The particle's motion at t=0 can be described by ____________.

a. an ellipse starting at time t=0 on the positive x axis
b. an ellipse starting at time t=0 on the positive y axis
c. a circle starting at time t=0 on the positive x axis
d. a circle starting at time t=0 on the positive y axis

2. When does the particle first cross the negative x axis?
Express your answer in terms of some or all of the variables omega, R, and pi.

3. Find the particle's velocity as a function of time.
Express your answer using unit vectors (e.g., A i+ B j, where A and B are functions of omega, R, t, and pi).

4. Find the speed of the particle at time t.
Express your answer in terms of some or all of the variables omega, R, and pi.

Answer 1

I will be happy to critique your thoughts. One comment: What is this x,y axis talk, the equation uses i,j axis.

Answer 2

it is the function r(t).

Answer 3

2. pi/w
3. -wRsin(wt)ihat +wRcos(wt)jhat
4.R*w

Answer 4

1. a circle starting at time on the positive x axis

Answer 5

1.
circle on x axis