Question

A wheel of mass 10 kg and radius 0.2 m is rotating at an angular speed of 100 rpm, when the motion is turned off. Neglecting the friction at the axis. Calculate the force that must be applied tangentially to the wheel to bring it to rest in 10 rev. Assumed wheel to be a disc.

Answer 1

Given :

       Mass(m) = 10kg

       Radius(r) = 0.2m

       Initial speed in rpm = 100rpm

                                 =100×(2π/60)rad/s   =10π/3 rad/s

To find :

      Force required to bring the wheel to rest in 10rev = ?

Solution:

• Change in angle of wheel(Δ∅) = 10×2π = 20π

• From equations of motion

                                ωf²-ωi² = 2αΔ∅

                                0²-(10π/3)² = 2α(20π)

                                α=0.87

• By the formula “Fr=Iα”

                         F(0.2)=mr²α/2

                         F=(10×0.2²×α)/0.4

                         F=0.4α/0.4

                         F=α =0.87N

The force applied on the wheel should be F=0.87N