(a) Show that the position of a particle on a circle of radius R with its center at the origin is r → = R (cos θî + sin θĵ ), where θ is the angle the position vector makes with the x -axis. (b) If the particle moves with constant speed v starting on the x -axis at t = 0, find an expression for θ in terms of time t and the period T to complete a full circle, (c) Differentiate the position vector twice with respect to time to find the acceleration, and show that its magnitude is given by Equation 3.16 and its direction is toward the center of the circle.
(a) Show that the position of a particle on a circle of radius R with its center at the origin is r → = R (cos θî + sin θĵ ), where θ is the angle the position vector makes with the x -axis. (b) If the particle moves with constant speed v starting on the x -axis at t = 0, find an expression for θ in terms of time t and the period T to complete a full circle, (c) Differentiate the position vector twice with respect to time to find the acceleration, and show that its magnitude is given by Equation 3.16 and its direction is toward the center of the circle.
(a) Show that the position of a particle on a circle of radius R with its center at the origin is
r
→
= R(cos θî + sin θĵ), where θ is the angle the position vector makes with the x-axis. (b) If the particle moves with constant speed v starting on the x-axis at t = 0, find an expression for θ in terms of time t and the period T to complete a full circle, (c) Differentiate the position vector twice with respect to time to find the acceleration, and show that its magnitude is given by Equation 3.16 and its direction is toward the center of the circle.
At a latitude of Φ=33°, at an altitude of 30000 km above the Earth's center, what is the acceleration vector of an object that completes 4 revolutions per day?
The velocity of a particle is V and is constant. It moves counterclockwise on a circle with center "O" and radius R.
Derivative of acceleration with respect to time; Find as a function of Ɵ, R, V, and the unit vectors (x^ , y^) in the x and y directions.
Hint: a = -V^2/R(cosƟx^+ sinƟy^) and dƟ/dt= V/R
Your answer is partially correct.
A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it
moves through the point at coordinates (4.90 m, 3.70 m) with a velocity of -2.40 î m/s and an
acceleration of +11.9 m/s². What are the (a) x and (b) y coordinates of the center of the circular path?
(a) Number i 4.41
(b) Number i
3.70
Unit
Unit
m
m
Chapter 3 Solutions
Essential University Physics: Volume 1 (3rd Edition)
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