Question

Express the angular velocity ω of the wheel in terms of the displacement d, the magnitude F of the applied force, and the moment of inertia of the wheel Iw, if you've found such a solution. Otherwise, following the hints for this part should lead you to express the angular velocity ω of the wheel in terms of the displacement d, the wheel's radius r, and α.

Answer 1

Answer:

The angular velocity of the wheel in terms of d, F, and I is,  ω = d/t (F/I α)    s⁻¹

Explanation:

Given,

The angular velocity ω

The displacement d

The magnitude of the applied force, F

The moment of inertia of the wheel I = mr²

The angular velocity can be written as

                         ω = v /r

where,

                     v - linear velocity

                      r - radius of the wheel

                          ω = d/t (1/r)               (∵ v = d /t)

The force can be written as,

                          F = m a

                              = m α r                  (∵ a = α r)

Multiplying both sides by r

                          F r = m r² α

                           F r = I α                     (∵ I = mr²)

                              r = I α / F

Substituting in the above equation for ω

                          ω = d/t (F/I α)    s⁻¹

Hence, the angular velocity of the wheel in terms of d, F, and I is,  ω = d/t (F/I α)    s⁻¹