Rotational Inertia.

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Presentation transcript:

Rotational Inertia

Equation F = ma a = rα F = mrα Στ = r ΣF = Σmr2α Moment of Inertia ( I ) – sum of rotational inertia of an object I = Σmr2 Στ = I α

Rotational Dynamics The distribution of mass matters here—these two objects have the same mass, but the one on the top has a greater rotational inertia, as so much of its mass is far from the axis of rotation. Top object is harder to start or stop rotating © 2014 Pearson Education, Inc.

Example Two small masses of 5.0kg and 7.0kg are mounted 4.0m apart on a light rod. Calculate the moment of inertia when rotated about the axis halfway between the weights.

Example Calculate the moment of inertia when the same two objects are rotated about an axis 0.50m to the left of the 5.0 kg mass.

For most objects, the calculation of the moment of inertia is very difficult However, for a number of regularly shaped objects, the expressions have already been worked out Pg. 210 in textbook

Example A fixed 0.15kg solid disk pulley with a radius of 0.075m is acted on by a net torque of 6.4N-m. What is the angular acceleration of the pulley?

Example What torque is needed to give a 20 kg solid ball with a radius of 0.20m an angular acceleration of 2.0 rad/s?

Example A 2000 kg Ferris wheel accelerates from rest to a angular speed of 2.0 rad/s in 12s. If the radius is 30m, what is the net torque on the wheel?

Example A 15.0N force is applied to a cord wrapped around a pulley of mass 4.00kg and radius 33.0 cm. The pulley accelerates form rest to an angular speed of 30.0 rad/s in 3.00 s. If there is a frictional torque of 1.10 m-N, determine the moment of inertia of the pulley.