Final answer:
The angular momentum of a 2.5 kg uniform cylindrical grinding wheel with a radius of 13 cm rotating at 1800 rpm is 0.0228 kg·m²/s.
Step-by-step explanation:
To calculate the angular momentum of a uniform cylindrical grinding wheel, we can use the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
The moment of inertia of a cylindrical grinding wheel is given by the formula I = 0.5mr², where m is the mass and r is the radius.
In this case, the mass of the grinding wheel is 2.5 kg and the radius is 13 cm. We first need to convert the radius to meters by dividing it by 100. So, the radius is 0.13 m.
Plugging the values into the moment of inertia formula, we get I = 0.5(2.5 kg)(0.13 m)².
Next, we need to convert the angular velocity from rpm to radians per second. To do this, we multiply the angular velocity by 2π/60. So, the angular velocity is (1800 rpm) * (2π/60).
Finally, we can calculate the angular momentum by multiplying the moment of inertia and angular velocity. L = (0.5(2.5 kg)(0.13 m)²) * (1800 rpm) * (2π/60).
Calculating the answer gives us L = 0.0228 kg·m²/s.