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Rotational Energy

Rotational Energy. Real objects have mass at points other than the center of mass. Each point in an object can be measured from an origin at the center of mass. If the positions are fixed compared to the center of mass it is a rigid body. Rigid Body. r i.

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Rotational Energy

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  1. Rotational Energy

  2. Real objects have mass at points other than the center of mass. Each point in an object can be measured from an origin at the center of mass. If the positions are fixed compared to the center of mass it is a rigid body. Rigid Body ri

  3. The motion of a rigid body includes the motion of its center of mass. This is translational motion A rigid body can also move while its center of mass is fixed. This is rotational motion. Translation and Rotation vCM 

  4. Kinematic equations with constant linear acceleration were defined. v = v0 + at x = x0 + v0t + ½at2 v2 = v02 + 2a(x - x0 ) Kinematic equations with constant angular acceleration are similar. w = w0 + at q = q0 + w0t + ½at2 w2 = w02 + 2a(q - q0 ) Rotational Motion

  5. A CD spins so that the tangential speed is constant. The constant speed is 1.3 m/s The inner radius is at 0.023 m The outer radius is at 0.058 m The total time is 74 min, 33 s = 4500 s Find the angular velocity at the beginning (inner) and end. Find the constant angular acceleration. Angular velocity is w=v/r. Inner: w = 1.3 m/s / 0.023 m =57 rad/s. Outer: w = 1.3 m/s /0.058 m =22 rad/s. Angular acceleration is Compact Disc

  6. Circular Energy • Objects in circular motion have kinetic energy. • K = ½ m v2 • The velocity can be converted to angular quantities. • K = ½ m (rw)2 • K = ½ (mr2) w2 • The term (mr2) is the moment of inertia of a particle.

  7. Integrating Mass • The kinetic energy is due to the kinetic energy of the individual pieces. • The form is similar to linear kinetic energy. • KCM = ½ mv2 • Krot = ½ Iw2

  8. How much energy is stored in the spinning earth? The earth spins about its axis. The moment of inertia for a sphere: I = 2/5 MR2 The kinetic energy for the earth: Krot = 1/5 MR2w2 With values: K = 2.56 x 1029 J Spinning Earth The energy is equivalent to 250 million times the world’s nuclear arsenal next

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