Laws of Motion Formula

Question

1.    How much mass must be added to an adjustable, empty dumbbell made to roll in order to gain a momentum similar to a rolling wheel with a mass of 40 kg at a velocity of 6.6 m/s? The dumbbell must be rolled at a fixed velocity of 10 m/s only.

Answer 1

Angular momentum is L=Iω=IV/R where I is moment of inertia, R is radius, ω is angular velocity, and V is linear velocity.

I _wheel= m_wheel (R_wheel)²   I _dumbbel= 0.5m_dumbbel (R_dumbbel)² +0.5m_dumbbel (R_dumbbel)²=m_dumbbel (R_dumbbel)

Then, by using equality between angular momenta,  I_dumbbelV_dumbbel/R_dumbbel = I_wheelV_wheel/R_wheel

Or   m_wheel (R_wheel)²V_wheel/R_wheel = m_dumbbel (R_dumbbel)²V_dumbbell/R_dumbbel

 Now, assume that   R_dumbbel = R_wheel, you can find m_dumbbel⁼ m_wheelV_wheel / V_dumbbell = (40 kg)(6.6 m/s)/10 m/s =26.4 kg