Final answer:
The angular momentum of a 3.2-kg cylindrical grinding wheel of radius 25 cm rotating at 1300 rpm is approximately 13.6 kg⋅m²/s, calculated using the moment of inertia for a solid cylinder and converting the angular velocity to radians per second.
Step-by-step explanation:
To find the angular momentum of a 3.2-kg uniform cylindrical grinding wheel with a radius of 25 cm rotating at 1300 rpm, we can use the formula for the angular momentum (L) of a rotating body:
L = I⋅ω
where:
- I is the moment of inertia of the cylinder, given by ½MR² for a solid cylinder.
First, we calculate the angular velocity in rad/s:
ω = 1300 revolutions/min × (2π rad/revolution) / (60 s/min) ≈ 136.1 rad/s
I = ½ × 3.2 kg × (0.25 m)² ≈ 0.1 kg⋅m²
Now we can compute the angular momentum:
L = 0.1 kg⋅m² × 136.1 rad/s ≈ 13.6 kg⋅m²/s
So, the angular momentum of the grinding wheel is approximately 13.6 kg⋅m²/s.