How do we describe Newton’s second law for rotation?

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Presentation transcript:

How do we describe Newton’s second law for rotation? HW:

What is Newton’s Second Law? F = ma So, what did we say is the rotational equivalent to force? TORQUE!!! We learned about torque earlier, but how can we describe it in terms of rotational motion? How did we write the rotational versions for ALL the kinematic equations??? This is the exact same equation that we learned before, but now we see how it matches all the other rotational ones!

Deriving a rotational expression for torque So now we have “τ = rF”, but if torque represents the 2nd law for rotation, then what about mass? How can we write force in terms of rotation? F = ma F = m x rα τ = mr2α Now we can substitute into the equation for torque!

Rotational Inertia τ = mr2 x α So, lets compare this to F = ma Torque is rotational force Angular acceleration is rotational acceleration (mr2) is rotational inertia with symbol “I”

Demo: Rotational Inertia Which has more rotational inertia “I”? Rotational motion measures how hard it is to change angular velocity. It’s based on mass and it’s distribution regarding the axis of rotation. ***Less rotational inertia means it’s easier to rotate an object just as less mass means it is easier to move an object. The cylinder is faster, so it must have less rotational inertia. It was easier to move!

Demo: Rotational Inertia Wands Which wand has less rotational inertia? Less rotational inertia means it’s easier to rotate an object just as less mass means it is easier to move an object.

Two weights on a bar: different axis, different “I” Two weights of mass 5 kg and 7 kg are mounted 4 m apart on a light rod (whose mass can be ignored). Calculate the moment of inertia when rotated about an axis halfway between the weights. I = Σmr2 I = (5kg)(2m)2 + (7kg)(2m)2 I = 48.0 kg.m2

Different Axis Calculate the moment of inertia now when rotated about an axis 0.5 m to the left of the 5 kg mass. How does the inertia added by the mass close to the axis compare to the mass farther away? I = Σmr2 I = (5kg)(.5m)2 + (7kg)(4.5m)2 I = 143 kg.m2

Summary What is Newton’s second law for rotational motion? How can we define rotational inertia? What affects the rotational inertia “I”? What was the difference between parts “a” and “b” in the practice questions? Torque = mr2 x angular acceleration or Torque = rF Measures an objects ability to rotate and change angular velocity. I = mr2 I depends on the axis of rotation and distribution of mass. Part “a” had both objects spread evenly from the axis and part “b” had one mass very close to the axis for a small “I”, but the other mass was very far away which yields a large “I”.