Rotational Kinetic Energy The rotational kinetic energy of
- Slides: 8
Rotational Kinetic Energy
The rotational kinetic energy of a rigid object depends on its: 1. Moment of inertia 2. Angular velocity For an object of moment of inertia I rotating uniformly at ω rad s-1 the rotational kinetic energy is given by: E(rot)k = ½Iω²
Example Using the example from the previous presentation for the girl on the roundabout calculate: a) the change in kinetic energy, b) explain this change in Kinetic energy.
a) Before E(rot)k = ½Iω²= 0. 5 x 1005 x 22 = 2010 J After E(rot)k = ½Iω²= 0. 5 x 645 x 3. 12 = 3100 J b) The increase in kinetic energy has come from the work done by the girl in moving in towards the centre.
Energy and Work Done If a torque T is applied through an angular displacement θ, then the work done = Tθ Doing work produces a transfer of energy, Tθ = ½Iω2 - ½Iω02 (work done = ΔEk).
Objects Rolling Down an Inclined Plane ω h θ v Note – Length of Slope = L. Therefore h = Lsinθ When an object such as a sphere or cylinder is allowed to run down a slope, the Ep at the top, (mgh), will be converted to both linear (½mv 2) and angular (½Iω2) kinetic energy.
An equation for the energy of the motion (assume no slipping) is given below. mgh = ½Iω2 + ½mv 2
Linear/Rotational Equivalence Linear Displacement, s Velocity, v Acceleration, a Mass, m Force, F Momentum, p Rotational Angular Displacement, θ Angular Velocity, ω Angular Acceleration, α Moment of Inertia, I Torque, T Angular Momentum, L
