Unit: NM 8 Topic(s): Rotational Inertia and Torque Learning Goals: Identify the physical factors that contribute to the moment of inertia for a rotating body Compare and Contrast linear dynamics with rotational dynamics Describe how net torque changes the angular velocity and angular momentum of a system

Putting a new spin on Newton’s 2nd Law With linear dynamics we had Fnet=ma. Our mass mass was our inertia and the object was uniform in consistency For rotational motion a net (or unbalanced) torque will cause an object to experience rotational acceleration The geometry of the mass matters

Moment of Inertia Sometimes called rotational inertia or just “moment” instead of just how many kgs (linear mass/inertia), it depends on where the mass is with respect to the axis of rotation Can be calculated for “unique” shapes. Equations exist for “normal” shapes.

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Frictional Torque Both static and kinetic opposes intended motion (static) or actual motion (kinetic). no set equation like linear friction

Solving Rotational Dynamics Problems Draw a diagram complete with torque “swoops” Write down gives and unknowns Write down τ= Iα Drop down Iα Collect torques on “torque side” Solve for unknowns Remember problems can be complex and there may be multiple steps to get to the ultimate solution

A 15 N force is applied to a cord wrapped around a pulley of mass M=4kg and radius R=33.0cm. The pullet accelerates uniformly from rest to an angular speed of 30 rad/s in 3s. There is a frictional torque of 1.1 N ⋅ m. What is the moment of inertia of the pulley?

A 2m long uniform rod is allowed to rotate through point P A 2m long uniform rod is allowed to rotate through point P. The rod has a mass of 3kg. What is the angular acceleration of this rod (I=1/3*M*l^2)?