The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity 𝜔₁. A rigid bar PQ is pinned to the wheel at P while the end Q slides on the floor.

What is the angular velocity 𝜔₂ of the bar PQ?

In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the 2 cm long link is ω₂ = 5 rad/s. Given the dimensions as shown, the magnitude of the angular velocity ω₄ of the 4 cm long link is given by rad/s (round off to 2 decimal places).

A planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figure, where AB ⊥ CE and FD ⊥ CE. The T-shaped link CDEF is constructed such that the slider B can cross the point D, and CE is sufficiently long. For the given lengths as shown, the mechanism is

Block 2 slides outward on link 1 at a uniform velocity of 6m/s as shown in the figure. Link 1 is rotating at a constant angular velocity of 20 radian/s counterclockwise. The magnitude of the total acceleration (in m/s² ) of point P of the block with respect to fixed point O is ____________