Rigid body rotations inertia. Constant angular acceleration.

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Presentation transcript:

Rigid body rotations inertia

Constant angular acceleration

Example Placed on a long incline, a wheel is released from rest and rolls for 30.0 s until it reaches a speed of 10.0 rad/s. Assume its acceleration is constant, what angle did it turn through?

Reading Assignment 9.4: The moment of inertia is A. the small time a body needs to react to an external force B. a measure of mass distribution concerning rotation C. equal to the mass of a rotating object D. the time between alarm clock and eye-opening

Determine the moment of inertia of a ruler that is rotating around an axis perpendicular to it through its center of mass. The ruler has length L and mass M.

Determine the moment of inertia of the same ruler, this time rotating around an axis through one of its ends. Parallel-axis theorem

Determine the moment of inertia for a solid disk of mass M, radius R and thickness h around a rotational axis through the center, as shown. What will be the moment of inertia for the disk, if it is rolling on the ground?

The following items all have the same radius and mass. Rank them from smallest to largest rotational inertia. Solid disk Solid cylinderHoop Hollow cylinderSphere

Rotational kinetic energy Translation Rotation

Energy conservation again Determine the final linear speed of a solid cylinder released from rest on an incline as it overcomes a height difference of h.