Part A Determine the velocity x-component of the particle at any time t. Express

Question

Part A
Determine the velocity x-component of the particle at any time t.
Express your answer in terms of some or all of the variables R, omega and t .

Part B
Determine the velocity y-component of the particle at any time t.
Express your answer in terms of some or all of the variables R, omega and t.

Part C
Determine the acceleration x-component of the particle at any time t.
Express your answer in terms of some or all of the variables R, omega and t .

Part D
Determine the acceleration y-component of the particle at any time t.
Express your answer in terms of some or all of the variables R, omega and t.

Part E
At which times is the particle momentarily at rest?
Express your answer in terms of the variables n, omega, and appropriate constants.

Explanation / Answer

Vx=R(w-wcoswt) Vy=R(wsinwt) Ax=R(w^2sinwt) Ay=R(w^2coswt) c) At rest for Vx=0 and Vy=0 Vx=0=R(w-wcoswt) ie. when coswt =1; wt =0, 2Pi, 4Pi... Vy=0=R(wsinwt) i.e. when sinwt =0; wt = Pi/2, 3Pi/2, 5Pi/2... Substitute these wt values into the x(t), y(t) equations to get the coordinates. d) The magnitude of the acceleration is Rw^2 and does not depend on time. Compared to uniform circular motion it is related by the speed of the vehicle if the vehicle speed were deducted then the motion would be circular.

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