Rotational Equilibrium and Dynamics

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Presentation transcript:

Rotational Equilibrium and Dynamics Rotational Dynamics

Newton’s Second Law for Rotation Newton’s Second Law of Motion for Rotating Objects net torque = moment of inertia * angular acceleration Τnet = Ια Positive torque causes counterclockwise rotation Angular acceleration is counterclockwise Negative torque causes clockwise rotation Angular acceleration is clockwise When net torque is zero, the wheel rotates with constant angular velocity

Angular Momentum Rotating objects have angular momentum The product of a rotating object’s moment of inertia and angular speed about the same axis Represented by L and measured in kilogram meters2 per second (kgm2/s) Angular momentum = moment of inertia * angular speed L = Ιω

Angular Momentum Law of conservation of angular momentum – when the net external torque acting on an object is zero, the angular momentum of the object does not change

Rotational Kinetic Energy Rotational kinetic energy – the energy of an object due to its rotational motion Measured in joules (J) Rotational kinetic energy = ½ * moment of inertia * angular speed2 KErot=½Ιω2

Rotational Kinetic Energy Mechanical energy is conserved with rotating objects Mechanical energy = translational kinetic energy + rotational kinetic energy + gravitational potential energy + elastic potential energy ME = KEtrans + KErot + PEg + PEelastic ME = ½mv2 + ½Ιω2 + mgh + ½kx2

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