Consider the motion of a point (or particle) on the circumference of a rolling circle. As the circle rolls, it generates the cycloid r(t) = b(ωt − sin ωt)i + b(1 − cos ωt)j where ω is the constant angular speed of the circle and b is the radius of the circle. Find the velocity and acceleration vectors of the particle. Use the results to determine the times at which the speed of the particle will be (a) zero and (b) maximized.
Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
Consider the motion of a point (or particle) on the circumference of a rolling circle. As the circle rolls, it generates the cycloid r(t) = b(ωt − sin ωt)i + b(1 − cos ωt)j where ω is the constant angular speed of the circle and b is the radius of the circle. Find the velocity and acceleration vectors of the particle. Use the results to determine the times at which the speed of the particle will be (a) zero and (b) maximized.
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