Exam 2

1. period of motion =T= (2 pi r)/v
   1. centripetal acceleration = ac = (v^2)/r
      1. spinning rate = w = v/r
2. used in many cases
   1. planet orbits, satellite orbits
   2. theme park ride: turns, loops and hills

1. Work= Force multiplied by the difference of x multiplied by cos of the angle
   1. Work is measure in Joules (J)
   2. W= Fxcos(angle)
2. Energy: Kinetic and Potential
   1. Kinetic Energy (KE)= 1/2 mv^2
   2. Potential Energy (PE)= mgh
   3. Mechanical Energy= mgh + 1/2 mv^2
3. E1 = E2
4. KEi + PEi = KEf + PEf

Attachments:

• Exam 1

1. Describing rotational motion
   1. Rotational Quantities
      1. Angular position = theta
         1. theta = (s/r) where s is arc length, r is radius
      2. Angular velocity = lowercase omega (fancy w)
         1. omega = theta/time
      3. Angular acceleration = alpha
         1. alpha = omega/time
   2. Radians
      1. 360 degrees = 2(pi) rad
2. Torque and Newton's Laws for rotational motion
   1. torque = Force * radius
   2. sigma torque = I * alpha
      1. moment of inertia = I = dependent upon object and shape
      2. Newton's second law for rotational motion
3. Rotational Equilibrium
   1. total torque = 0
4. Rotational Dynamics
   1. delta theta = (angular velocity)(delta time) + 1/2(alpha)(delta time ^2)
      1. final angular velocity = (initial ang velocity) + (alpha)(delta time)
   2. (ang velocity final ^2) = (ang velocity initial ^2) + 2(alpha)(delta theta)
5. Combined Rotational and Translational Motion
   1. Arises in many cases
      1. a rolling wheel
      2. motion of a baseball bat
   2. Rolling Motion
      1. angular v * R = v = 2(pi)R / T
      2. a = alpha * R
   3. base ball bat scenario
      1. more complex than rolling motion
         1. involves linear and rotational:
            1. quantities, dynamics, and center of mass

1. Momentum
   1. Momentum(P) = mass x velocity
   2. Momentum is conserved during collisions
2. Impulse
   1. Impulse is the change in time multiplied by the force in question. This is the same as the change in momentum.
3. Collisions
   1. Elastic collisions
      1. Kinetic energy is conserved
      2. KE1f+KE2f = KEi1+KEi2
      3. momentum is conserved
   2. Inelastic collisions
      1. Kinetic energy is not conserved
      2. KE1f+KE2f not equal to KE1i+KE2i
      3. Vf = (m1v1i + m2v2i)/(m1+m2)
      4. momentum is conserved
   3. Kinetic energy = 1/2 mv
   4. completely inelastic collisions
      1. objects stick together after collisions
         1. momentum still conserved