Torque and Rotational Dynamics

A bicycle wheel with a radius of 0.5 m rotates through an angle of $2\pi$ radians. What is the arc length traveled by a point on the edge of the wheel?

A wheel with a radius of 0.3 m rotates through an angle of 6 radians. What is the arc length traveled by a point on the edge of the wheel?

A point on the edge of a rotating disk travels an arc length of 1.5 meters. If the radius of the disk is 0.5 meters, through what angle (in radians) has the disk rotated?

A wheel with a radius of 0.4 m rolls without slipping and completes 5 full rotations. How far has the center of the wheel traveled?

A point on a rotating object is 0.2 m from the axis of rotation. If the object has an angular velocity of 10 rad/s, what is the linear velocity of the point?

A rotating object has a point located 0.4 m from its center. This point has a linear velocity of 6 m/s. What is the angular velocity of the rotating object?

A disk is rotating such that its angular velocity changes with time according to the equation $\omega(t) = 2t^2 + 3t$ (in rad/s). A point on the disk is 0.5 m from the center. What is the tangential acceleration of this point at t = 2 s?

A rigid disk is rotating. Which statement accurately compares the angular and linear velocities of points at different distances from the center?

Two points, A and B, are located on a rotating disk. Point A is 0.2 m from the center, and point B is 0.4 m from the center. If point A has a linear velocity of 2 m/s, what is the linear velocity of point B?

Two gears are connected such that the smaller gear (radius $r_1$) drives the larger gear (radius $r_2$). If the smaller gear has an angular velocity of $\omega_1$, what is the angular velocity $\omega_2$ of the larger gear?