A ball is rolling with a constant angular speed around a circular groove in the

Question

A ball is rolling with a constant angular speed around a circular groove in the surface of a horizontal table. If the angular speed is 2.3 rad/s in the counterclockwise direction, the radius of the circular groove is 0.57 m, and the angular position of the ball at t = 0 is = 0, determine the x component of the ball's position at the times 1.0 s, 4.0 s, and 5.5 s. (Assume = 0 lies along the +x axis.

x(t = 1.0 s) =_____ m

x(t = 4.0 s) =_____ m

x(t = 5.5 s) =_____ m

x(t = 1.0 s) =_____ m

x(t = 4.0 s) =_____ m

x(t = 5.5 s) =_____ m

Explanation / Answer

Here,

w = 2.3 rad/s

at time , t = 1 s

x(t = 1) = r * cos(w * t)

x(t = 1) = 0.57 * cos(1 * 2.3)

x(t = 1) = -0.38 m

at time t= 4 s

x(t = 4) = r * cos(w * t)

x(t = 4) = 0.57 * cos(4* 2.3)

x(t = 4) = -0.56 m

at time t = 5 s

x(t = 5) = r * cos(w * t)

x(t = 5) = 0.57 * cos(5 * 2.3)

x(t = 5) = 0.28 m

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