A boy on a merry-go-round at a distance of 1.25 m from the center. If the boy moves through an arc length of 2.25 m, through what angular displacement does he move?

A child sits on a merry‑go‑round that has a diameter of 6.00 m. The child uses her legs to push the merry‑go‑round, making it go from rest to an angular speed of 18.0 rpm in a time of 37.0 s. What is the angular displacement Δθ of the merry‑go‑round, in units of radians (rad), during the time the child pushes the merry‑go‑round?

A small object with mass 4.15 kg moves counterclockwise with constant angular speed 1.30 rad/s in a circle of radius 3.30 m centered at the origin. It starts at the point with position vector 3.301 m. Then it undergoes an angular displacement of 9.30 rad. (a) What is its new position vector? m (b) In what quadrant is the object located and what angle does its position vector make with the positive x-axis? ---Select--- ✓ at (c) What is its velocity? m/s (d) In what direction is it moving? (Give a negative angle.) • from the +x direction. (e) What is its acceleration? m/s² (f) What total force is exerted on the object? N

The blades on an electric blender are moving with an angular velocity of 296.8 radians/s. When the blend button is pressed, the blades accelerate at a constant value of 302.7 rdians/s^2. Find the angular velocity of the blades after they have moved through an angular displacement of 75.9 rad (radians) with this angular acceleration. Note the unit of radians is abbreviated as rad.