Answer:
9.0 N
Explanation:
The location of the mass of the wheel on the wheel = Evenly distributed
The acceleration of the solid wheel, α = 3.25 rad/s²
The applied force on the wheel = 4.5 N
The location mass of the replacement wheel = All on (around) the rim
The moment of inertia of the new wheel, I = m·r² (From an online source)
We have;
The moment of inertia for a solid wheel = 1/2·m·r²
The torque, τ = Moment of inertia, I × Acceleration, α
For the solid wheel, we have;
τ = 1/2·m·r² × 3.25 rad/s²
τ = r × F = r × m × a
For the replacement wheel, we have;
τ = m·r² × 3.25 rad/s² = 2 × 1/2·m·r² × 3.25 rad/s²
∴ τ = 2 × r × F
Given that the radius remains the same, the force applied on the replacement wheel needs to be doubled
The force that should be exerted on the strap to give the same angular velocity, F' = 2 × F
The required force, F' = 2 × 4.5 N = 9.0 N.
