Question

a ball rolls on a circular track of radius 0.62m with a constant angular speed of 1.3 rad/s in the counterclockwise direction. If the angular position of the ball at t=0 is angle = 0, fin the x component of the ball's position at the time 2.5s, 5.0s, 7.5s. Let theda =0 correspond to the positive x direction.

Answer 1

At time 2.5 second

radθ=1.3 rad/s*2.5 sec= 3.25 rad *180 deg/π rad = 186.2 degrees

x = 0.062 m * cos 186.2 = -0.62 m

at 5 seconds

rad = 1.3 * 5 = 6.5 rad * 180 deg/πrad = 372 deg

x = 0.62 m * cos (372-360) = 0.61 m

*full circle 360 degrees.

at 7.5 sec

rad = 1.3*7.5 = 9.75 rad = 558.6 deg

x = 0.62*cos(558.6-360) = -0.59 m