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Physics with Calculus - Exam 1 Practice Concepts

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Terms in this set (20)

  • Equation for velocity with constant acceleration
    Velocity is given by \(v_f = v_i + at\), where v_f is final velocity, v_i initial velocity, a acceleration, and t time.
  • Equation for position with constant acceleration
    Position is \(x = x_i + v_i t + \frac{1}{2} a t^2\), where x_i is initial position.
  • Formula for acceleration from velocity and time
    Acceleration is \(a = \frac{\Delta v}{\Delta t}\), the change in velocity over change in time.
  • Newton's Second Law
    Force is \(\vec{F} = m \vec{a}\), where m is mass and a acceleration.
  • Kinetic energy formula
    Kinetic energy is \(K = \frac{1}{2} m v^2\), where m is mass and v velocity.
  • Potential energy near Earth's surface
    Potential energy is \(U = m g y\), where g is gravitational acceleration and y height.
  • Work done by a force
    Work is \(W = \int \vec{F} \cdot d\vec{r}\), the integral of force over displacement.
  • Impulse-momentum theorem
    Impulse \(\vec{J} = \int \vec{F} dt = \Delta \vec{p}\), equals change in momentum.
  • Angular velocity and linear velocity relation
    Linear velocity \(v = r \omega\), where r is radius and \(\omega\) angular velocity.
  • Rotational kinetic energy
    Rotational kinetic energy is \(K = \frac{1}{2} I \omega^2\), where I is moment of inertia.
  • Torque and angular acceleration
    Torque is \(\vec{\tau} = I \vec{\alpha}\), where \(\alpha\) is angular acceleration.
  • Period of a simple pendulum
    Period is \(T = 2 \pi \sqrt{\frac{\ell}{g}}\), where \(\ell\) is length and g gravity.
  • Relationship between vectors S, M, and N in the triangle
    From the figure, S = M - N.
  • Value of sin 53°
    From the trig table, sin 53° = 4/5.
  • Value of cos 37°
    From the trig table, cos 37° = 4/5.
  • Value of tan 30°
    From the trig table, tan 30° = \(\sqrt{3}\)/3.
  • Acceleration of ISS relative to g
    The ISS acceleration is approximately 0.88 g.
  • Initial speed for projectile landing 100 m away at 53°
    Initial speed is about 32 m/s.
  • Time for hay bale to fall from 180 m
    Time to land is about 6.1 seconds.
  • Distance between hay bales dropped every 2 seconds at 50 m/s
    Distance between bales is about 100 m.