Rolling motion (without slipping)
Rigid body dynamics · Physics
Simple pendulum
Interactive 3DRelease the bob and watch true small-angle SHM. The period depends only on the string length.
Controls
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Study notes
Problem: A solid sphere of mass 2 kg and radius 0.1 m rolls without slipping on a flat surface with a linear velocity of 2 m/s. Calculate the total kinetic energy of the sphere. Steps: 1. Identify the two components of kinetic energy: Translational (KE_t) and Rotational (KE_r). 2. Calculate Translational KE: KE_t = 0.5 * m * v^2. Here m=2, v=2. So, KE_t = 0.5 * 2 * 2^2 = 0.5 * 2 * 4 = 4 Joules. 3. Calculate Angular velocity (omega): For rolling without slipping, v = r * omega. So, omega = v / r = 2 / 0.1 = 20 rad/s. 4. Calculate Moment of Inertia (I) for a solid sphere: I = (2/5) * m * r^2. I = 0.4 * 2 * 0.1^2 = 0.4 * 2 * 0.01 = 0.008 kg m^2. 5. Calculate Rotational KE: KE_r = 0.5 * I * omega^2. KE_r = 0.5 * 0.008 * 20^2 = 0.5 * 0.008 * 400 = 1.6 Joules. 6. Total KE = KE_t + KE_r = 4 + 1.6 = 5.6 Joules.