- #1
IsakVern
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- TL;DR Summary
- When they have equal kinetic energy but not equal angular momentum?
Assume that a kick-scooter rolls on a smooth surface without slipping, and that - for simplicity - all the mass of the scooter's two wheels are distributed like a loop/ring, i.e. around the edges of the wheels with no mass in the centre of the wheels. The wheels have radius R and the scooter is traveling with speed v.
Will another scooter traveling at the exact same speed, with wheels of the exact same mass, but with radii 2R be harder to stop? Because they will have equal kinetic energy but not equal angular momentum.Kinetic Energy:
Scooter 1: KE = 1/2mv2 + 1/2Iw2 = 1/2mv2 + 1/2*mR²*(v/R)² = mv2
Scooter 2: KE = 1/2mv2 + 1/2Iw2 = 1/2mv2 + 1/2*m*(2R)²*(v/2R)² = mv2
Angular momentum:
Scooter 1: L = Iw = mR²*(v/R) = mRv
Scooter 2: L = Iw = m*(2R)²*(v/2R) = m*4R²*v/(2R) = 2mRv
Will another scooter traveling at the exact same speed, with wheels of the exact same mass, but with radii 2R be harder to stop? Because they will have equal kinetic energy but not equal angular momentum.Kinetic Energy:
Scooter 1: KE = 1/2mv2 + 1/2Iw2 = 1/2mv2 + 1/2*mR²*(v/R)² = mv2
Scooter 2: KE = 1/2mv2 + 1/2Iw2 = 1/2mv2 + 1/2*m*(2R)²*(v/2R)² = mv2
Angular momentum:
Scooter 1: L = Iw = mR²*(v/R) = mRv
Scooter 2: L = Iw = m*(2R)²*(v/2R) = m*4R²*v/(2R) = 2mRv