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
