A grinding wheel has a mass of 250 kg and moment of inertia of 500 kg m².A torque of 100 N.m is applied to the grinding wheel.If the wheel starts from rest,what is the angular momentum of the wheel after 5.0 seconds? A) 650 kg m²/s B) 500 kg m²/s C) 450 kg m²/s D) 300 kg m²/s E) 250 kg m²/s

Question

Quizplus · Accepted Answer

Angular momentum (L) = moment of inertia x angular velocity (ω)
Initial angular velocity (ω) = 0 (since the wheel starts from rest)
Torque (τ) = rate of change of angular momentum (dL/dt) = moment of inertia x angular acceleration (α)
α = τ/I
Using the equations of rotational kinematics:
ω = αt = (τ/I)t
Substituting the given values:
angular velocity ω = (100 Nm) / (500 kg m2) x (5.0 s) = 0.1 rad/s
L = 500 kg m2 x 0.1 rad/s = 50 kg m2/s = 500 kg m/s
Therefore, the angular momentum of the wheel after 5.0 seconds is 500 kg m2/s, which corresponds to choice B.

A Grinding Wheel Has a Mass of 250 Kg and Moment