Physics

Uniform Circular Motion:

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.

  1. 👍 0
  2. 👎 0
  3. 👁 3,060
  1. I will be happy to critique your thoughts. One comment: What is this x,y axis talk, the equation uses i,j axis.

    1. 👍 0
    2. 👎 0
  2. it is the function r(t).

    1. 👍 0
    2. 👎 0
  3. 2. pi/w
    3. -wRsin(wt)ihat +wRcos(wt)jhat
    4.R*w

    1. 👍 2
    2. 👎 0
  4. 1. a circle starting at time on the positive x axis

    1. 👍 0
    2. 👎 0
  5. 1.
    circle on x axis

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    The vector position of a particle varies in time according to the expression r with arrow = 6.60 i − 9.00t2 j where r with arrow is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a

  2. physics

    The velocity-versus-time graph is shown for a particle moving along the x-axis. Its initial position is x0 = 1.8m at t0 =0s. Part A What is the particle's position at t=1.0s? Part B What is the particle's acceleration at t= 1.0s?

  3. Physics HELP!

    The position of an object connected to a spring varies with time according to the expression x = (7.1 cm) sin (2.1π t). Find (a) the period of this motion (b) the frequency of the motion (c) the amplitude of the motion (d) the

  4. Physics HELP

    1.If a particle moves in a plane so that its position is described by the functions x=A*cos(wT) and y=A*sin(wT), the particle is ( w-angular velocity, T-period) A) moving with constant speed along a circle B) moving with a varying

  1. physics

    For this problem use the Uniform circular motion mode of the simulation. (a) Given the limits on the sliders in the simulation, what is the maximum possible speed that can be achieved in "Uniform circular motion" mode? .25 m/s For

  2. manetism help!

    A charged particle with charge q is moving with speed v in a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendiculuar to the same magnetic field. The time to complete one full circular

  3. Physics

    To find the velocity and acceleration vectors for uniform circular motion and to recognize that this acceleration is the centripetal acceleration. Suppose that a particle's position is given by the following expression: r(t) =

  4. Physics 2

    A particle moves along a line where the potential energy of its system depends on its position r as graphed in Figure P8.46. In the limit as r increases without bound, U(r) approaches +1 J. (a) Identify each equilibrium position

  1. Physics

    A charged particle is projected into a uniform B-field. Its velocity vector is perpendicular to the B-field vector. What type of path will the particle travel? Neglect gravity. Answer straight line motion elliptical motion

  2. physics

    Particle 1 and particle 2 have masses of m1 = 1.5×10-8 kg and m2 = 6.2×10-8 kg, but they carry the same charge q. The two particles accelerate from rest through the same electric potential difference V and enter the same

  3. physics

    the motion of a particle along a straight line is described by the function x=(2t-3)^2 where x is in metres and t is in seconds. A)find the position ,veocity and acceleration at t=2 sec. B) find the velocity of the particle at

  4. Calculus

    The position function of a particle in rectilinear motion is given by s(t) = 2t^3 – 21t^2 + 60t + 3 for t ≥ 0. Find the position and acceleration of the particle at the instant the when the particle reverses direction. Include

You can view more similar questions or ask a new question.