- #1
HeLLz aNgeL
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Suppose that a particle's position is given by the expression in the attachment
Explain:
1. When does the particle first cross the negative x axis?
2. Find the particle's velocity as a function of time. Express your answer using unit vectors.(e.g., A i_unit+ B j_unit, where A and B are functions of omega, R, t, and pi).
3. Find the speed of the particle at time t. Express your answer in terms of some or all of the variables.
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.
5. Now find the acceleration of the particle. Express your answer using unit vectors (e.g., A i_unit+ B j_unit, where A and B are functions of omega, R, t, and pi).
6. Your calculation is actually a derivation of the centripetal acceleration. To see this, express the acceleration of the particle in terms of its position r_vec(t).
Express your answer in terms of some or all of the variables r_vec(t) and omega.
ok, i know that omega gives you the angular velocity, but i don't understand how that factors into the "i" and "j" equations... are they the x, and y-axis components ? if they are do i have to plug in values one-by-one to check when it crosses the negetive x-asis ?
i'm confused !
Explain:
1. When does the particle first cross the negative x axis?
2. Find the particle's velocity as a function of time. Express your answer using unit vectors.(e.g., A i_unit+ B j_unit, where A and B are functions of omega, R, t, and pi).
3. Find the speed of the particle at time t. Express your answer in terms of some or all of the variables.
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.
5. Now find the acceleration of the particle. Express your answer using unit vectors (e.g., A i_unit+ B j_unit, where A and B are functions of omega, R, t, and pi).
6. Your calculation is actually a derivation of the centripetal acceleration. To see this, express the acceleration of the particle in terms of its position r_vec(t).
Express your answer in terms of some or all of the variables r_vec(t) and omega.
ok, i know that omega gives you the angular velocity, but i don't understand how that factors into the "i" and "j" equations... are they the x, and y-axis components ? if they are do i have to plug in values one-by-one to check when it crosses the negetive x-asis ?
i'm confused !