Energy Revisited. Types of Energy Kinetic energy: Energy due to motion of the center of mass of an object. Potential energy: Energy due to the position.

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Angular Quantities Correspondence between linear and rotational quantities:

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Presentation transcript:

Energy Revisited

Types of Energy Kinetic energy: Energy due to motion of the center of mass of an object. Potential energy: Energy due to the position of the center of mass of an object. But something’s missing…

Rotational Kinetic Energy Consider a flat object rotating freely about an axis.

Energy in a Wind Turbine We can approximate each blade of Length L and mass m as a thin rod rotating around its end. So for every blade…. What energy is stored in a three- blade wind turbine? Assume that the turbine rotates at a constant 45 RPM (4.7 rad/s), and that each blade is 2 m long and has a mass of 5 kg.

Energy Conservation Revisited If W nc = 0, and there are no other conservative forces present, we have conservation of energy.

Loop the loop What is the minimum h so that the cart makes it around the loop? From conservation of energy… What if the “cart” is a solid sphere instead?

Ramp Race Three objects roll down a ramp – a solid sphere, a hollow cylinder, and a solid cylinder. Which one wins?

Ramp Race Three objects roll down a ramp – a solid sphere, a hollow cylinder, and a solid cylinder. Which one wins?

Angular Momentum

We’ve been able to make a direct connection between linear quantities and angular quantities:

Angular Momentum An easy conversion between linear momentum and angular momentum can be made. Linear Motion Rotational Motion If no net external torque Another conserved quantity! Linear momentum (if no net external force) Mechanical energy (if no work by non-conservative forces) Angular momentum (if no net external torque)

Angular Momentum Example Two children ride a merry-go-round which is spinning at 20 rpm. The ride has a mass of 50 kg and a radius of 3 meters. Child A has a mass of 30 kg and sits a distance of 2 meters from the center. Child B has a mass of 45 kg and sits a distance of 2.5 meters from the center. At the same time, each child stands up and moves 1 meter closer to the center. What happens to the merry-go-round?