ROM - Rotational Kinematics

Rotational Kinematics

When a rigid object rotates around an axis we must discuss motion in terms of something besides the linear displacement. We define the angular displacement in terms of how far around the circular pathway it travels.

The angular displacement is measured in radians where one radian is equal to an arc length of one radius. From that definition we can follow the same steps as we did in kinematics to determine an angular velocity and an angular acceleration.

The rotational kinematic equations mirror those of linear kinematics. Rotational kinetic energy is the sum of the kinetic energy of the particles that make up the rigid rotating object.

Rotational kinetic energy introduces a concept called the moment of inertia. The moment of inertia depends on the mass of an object, the distribution of the mass, and the axis of rotation of the object.

Please watch the following presentation that will discuss Rotational Kinematics.

Rotational Kinematics Practice

We will now practice solving problems using the concepts you learned in the presentation. Make sure that you show all your work when you solve your problems. The presentation will give you time to work through the problems, find a solution, and check your work.

Use the chart below to determine different moments of inertia to use when solving problems in this module.

Moments of Inertia of Uniform Bodies Links to an external site.

Rotational Kinematics Self-Assessment

Now it is your turn. Complete the self-assessment questions to verify that you can apply the concepts of Rotational Kinematics.

A record player turntable playing at 33.3 rev/min is turned off. It takes 25s to come to rest.
1. What is the initial angular velocity of the turntable in rad/s?
2. What was the angular acceleration of the turntable assuming that it was constant?
3. What was the angular displacement of the turntable during this time?
4. If the turntable has a radius of 15 cm, what was the tangential acceleration of a point on the edge of the turntable?
5. If the turntable has a mass of 0.50 kg, how much work was done to bring it to a stop?

SOLUTIONS Links to an external site.

Four particles each with a mass of 2 kg are placed at the corners of a square 3 m on a side. They are connected by massless rods so that they maintain their shape. They are rotated around the z-axis using the bottom left mass as the point of rotation. What is the moment of inertia of the system? Assume that the particles sit in the xy plane.

Problem 2 Image