A particle moving in a circle of radius 15 cm makes 33.3 rev/min. If the particle starts on the positive x axis at time t = 0, what is the x component of the particle's velocity at time
T = 1.2 s?
A) 45 cm/s
B) -3.8 cm/s
C) 26 cm/s
D) -45 cm/s
E) 13 cm/s

Question

Quizplus · Accepted Answer

The particle's velocity is tangent to the circle, so its x component is given by:$$v_x = v \cos(\omega t)$$where v is the speed of the particle, $\omega$ is the angular velocity, and t is the time.The speed of the particle is:$$v = r\omega = (0.15 	ext{ m})(33.3 	ext{ rev/min})(2\pi 	ext{ rad/rev})(1 	ext{ min/60 s}) = 3.33 	ext{ m/s}$$The angular velocity of the particle is:$$\omega = 33.3 	ext{ rev/min}(2\pi 	ext{ rad/rev})(1 	ext{ min/60 s}) = 3.51 	ext{ rad/s}$$At time t = 1.2 s, the x component of the particle's velocity is:$$v_x = v \cos(\omega t) = (3.33 	ext{ m/s})\cos((3.51 	ext{ rad/s})(1.2 	ext{ s})) = 2.60 	ext{ m/s} = 26 	ext{ cm/s}$$

A Particle Moving in a Circle of Radius 15 Cm