ROM - Rotational Dynamics

Rotational Dynamics

Objects rotate when a force is applied away from the pivot point or center of mass of an object. Force applied at a distance from the pivot point is called the torque and depends on the value of the force, the distance from the pivot point, and the angle between the force and the radius.

Newton's second law for a rotating object states that the sum of the torque on an object is equal to the inertia of the object times its angular acceleration.

Please watch the following presentation that will discuss Rotational Dynamics. 

Rotational Dynamics Practice

Remember when solving these problems the relationship between linear quantities and angular quantities. Please watch the following presentation of some example problems.

Rotational Dynamics Self-Assessment

Now it is your turn. Complete the following Rotational Dynamics problems to verify that you understand how to solve these problems.

  1. A pulley system is composed of two pulleys that rotate together.  The first pulley has a mass of 10 kg and a radius of 0.50 m.  The second pulley has a mass of 5kg and a radius of 0.20 m.
    1. A force of 75 N is applied perpendicular to the radius of the larger pulley, how much force must be applied perpendicular to the small pulley to prevent the pulleys from rotating? Rollover image for the solution.
    2. If the value of the force is reduced to 100 N, what will be the magnitude and direction of the acceleration of the system? 

Problem 1 Image

SOLUTIONS Links to an external site.

  1. A pulley with a mass of 25kg and a radius of 15 cm has a massless rope placed over it.  A mass of 10kg is placed on the left end of the rope, and a mass of 20kg is placed on the right end of the rope. What is the acceleration of either mass? What is the tension on each side of the rope? 

Problem 2 Image

SOLUTIONS Links to an external site.

  1. A force of 60 N is applied at a tangent to the arc of a spherical solid with a mass of 30kg and a radius of 0.75m.  
    1. What is the angular acceleration of the sphere if it is free to rotate around its center?
    2. What will be the angular displacement of the sphere after 10s if the sphere starts from rest?
    3. What will be the angular velocity of the sphere after 10s?

SOLUTIONS Links to an external site.

Rotational Dynamics Practice Problems

Download Rotational Dynamics Practice Problems Links to an external site. for more practice. 

Download solutions Links to an external site. to the practice problems. 

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