Final answer:
To find the angular momentum of the bike's front wheel, calculate the moment of inertia using the mass and the radius, and then relate the wheel's linear velocity to its angular velocity to find the angular momentum.
Step-by-step explanation:
To calculate the angular momentum of the front wheel of a mountain bike, we need to use the formula for angular momentum L, which is L = Iω, where I is the moment of inertia and ω (omega) is the angular velocity. The moment of inertia for a hoop (like a bike wheel) is I = mr2, where m is the mass of the wheel and r is the radius. Given the mass m = 750 g = 0.75 kg and the radius r = 35 cm = 0.35 m, we can calculate the moment of inertia of the wheel.
To find the angular velocity, we need to relate the linear velocity v of the bike to the angular velocity using the formula v = rω. The linear velocity given is v = 10.0 m/s. Solving for ω, we get ω = v / r. Now we can insert the values for I and ω into the angular momentum formula to find the angular momentum of the wheel.
The calculated angular momentum will provide the value of the spinning wheel's momentum in the air the moment the bike leaves the ground.