Grade 11Mechanics
Plz answer the attached question....how to solve?????
Plz answer the attached question....how to solve?????
1 Answer
Arun
initial kinetic energy = 1/2 I ω² = 1/2 m r² ω²
I = moment of inertia of hoop of radius r and mass m. = m r²
ω = angular velocity.
initially the center of mass is not moving.
I = moment of inertia of hoop of radius r and mass m. = m r²
ω = angular velocity.
initially the center of mass is not moving.
let the hoop rotate and roll on the surface with an angular velocity = ω1
So its kinetic energy when it rolls = 1/2 I ω1² + 1/2 m (rω1)²
1/2 m r² ω² = 1/2 m r² ω1² + 1/2 m r² ω1²
ω² = 2 ω1² =>
ω1 = ω /√2
so velocity v = r ω1 = r ω/ 2
So its kinetic energy when it rolls = 1/2 I ω1² + 1/2 m (rω1)²
1/2 m r² ω² = 1/2 m r² ω1² + 1/2 m r² ω1²
ω² = 2 ω1² =>
ω1 = ω /√2
so velocity v = r ω1 = r ω/ 2
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