Calculus-based AP Physics C mechanics concepts including rotational dynamics and gravitation, beyond the algebra-based AP Physics 1 scope.
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- Write the definition of instantaneous velocity using calculus.
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v = dx/dt, the derivative of position with respect to time- Write the definition of instantaneous acceleration using calculus.
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a = dv/dt = d2x/dt2, the derivative of velocity with respect to time- If you know velocity v(t), how do you find position x(t)?
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Integrate: x = integral of v dt + x_0- If you know acceleration a(t), how do you find velocity v(t)?
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Integrate: v = integral of a dt + v_0- State the work-energy theorem.
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Net work done on an object equals its change in kinetic energy: W_net = delta KE- Write Newton's law of universal gravitation.
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F = GMm/r2, where G is gravitational constant, M and m are masses, r is distance- Write gravitational potential energy in the general form.
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U = -GMm/r, taking U = 0 at r = infinity- Define escape velocity.
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Minimum speed to escape a body's gravitational field without further propulsion- Relate escape velocity to orbital velocity.
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v_escape = sqrt(2) times v_orbital- State Kepler's third law for orbital motion.
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T2 = (4*pi2/GM)*r3, or T2 proportional to r3- Define torque using force and position vector.
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tau = r cross F = rF sin(theta), where theta is angle between r and F- Define moment of inertia for a point mass distribution.
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I = sum of (m_i * r_i2) for each mass element- State the parallel axis theorem.
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I_parallel = I_cm + M*d2, where d is distance between parallel axes- Write the formula for rotational kinetic energy.
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KE_rot = (1/2)*I*omega2- Define angular momentum for a point particle.
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L = r cross p = r cross (mv) = mrv sin(theta)
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