Joey, whose mass is m = 36 kgkg, stands at rest at the outer edge of a frictionless merry-go-round with the mass M = 200 kgkg and the radius R = 2.0 mm, as in (Figure 1). The merry-go-round is also at rest. Joey then begins to run around the perimeter of the merry- go-round, finally reaching a constant speed, measured relative to the ground, of 4.0 m/sm/s. What is the final angular speed of the merry-go-round? Express your answer in radians per second.

One end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m, as shown in the figure below. When θ = 23.0°, the speed of the object is 5.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An arrow labeled vector v points in the direction of motion. (a) At this instant, find the magnitude of the tension in the string.Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N(b) At this instant, find the tangential and radial components of acceleration. at = Your response differs from the correct answer by more than 100%. m/s2 downward tangent to the circle ac = Your response differs from the correct answer by more…

In the figure here, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance d from the right edge of the plateau. The vertical heights are h, = 3.5 cm and h2 = 1.70 cm. With what speed must the ball be shot at point P for it to land at d = 4.5 cm? Ball

In the figure, a solid 0.1 kg ball rolls smoothly from rest (starting at height H = 6.3 m) until it leaves the horizontal section at the end of the track, at height h = 2.0 m. How far horizontally from point A does the ball hit the floor? Number Units