Answer:
First, we need to find the torque applied to the wheel. The torque formula is given by:
τ = r × F × sin(θ)
where
r = radius of the wheel = 50 cm = 0.5 m
F = force applied tangentially = 20 N
θ = angle between the force and the radius (which is 90 degrees for a tangential force)
So, τ = 0.5 × 20 × sin(90) = 10 Nm
The moment of inertia of a solid cylinder (which the wheel can be approximated to) is given by:
I = 0.5 × m × r^2
where
m = mass of the wheel = 2.5 kg
r = radius of the wheel = 0.5 m
So, I = 0.5 × 2.5 × 0.5^2 = 0.3125 kgm^2
The angular acceleration can be calculated using the formula:
α = τ / I
So, α = 10 / 0.3125 = 32 rad/s^2 (rounded to two decimal places)
Therefore, the angular acceleration when a force of 20N is applied tangentially to the tire of a 2.5 kg bicycle wheel with a radius of 50cm is 32 rad/s^2.