![]() Calculate various forms of work such as rotational, force over distance and force. An object may be cruising along at velocity, say v, thus having a translational kinetic energy K T 1 2 m v 2. (This requires some unusual identities that I've seen before, but never really learned. Calculate work, inclined plane, circular motion and rolling motion. Cross radius into both sides and then play around with the algebra. Calculate the angular acceleration produced (a) when no one is on the merry-go-round and (b) when an 18.0-kg child sits 1.25 m away. Dynamics is concerned with force and mass and their effects on motion. Movement equations describe the behavior of a physical system in terms of dynamic variables as a series of mathematical functions. Dynamics for rotational motion is completely analogous to linear or translational dynamics. What causes the rotation Equations of motion Motion equations are equations that define a physical system's action as a function of time, in terms of its motion. Start with the equation for Newton's second law. MAKING CONNECTIONS: ROTATIONAL MOTION DYNAMICS. ![]() Translational and rotational quantities compared concept (Here action and reaction refer to torques.) Step 2: Using the equation r F sin for calculating torque, write an equation summing all of the torques acting on the object. ![]() But since the radius of each gear could be different, there can't be some global sum torque acting on all of them equally, which means there has to be a global sum force. (Here action and reaction refer to forces.)įor every action there is an equal and opposite reaction. It seems strange that the evolution of a rotational system is expressed only in linear units. is the moment of inertia, and is the angular acceleration. For the purposes of calculating the torque due to the gravitational force, you can assume all the force acts at a. Use Newton’s second law and also the rotational version of Newton’s second law: Net Torque. Taste and compare… Translational and rotational laws of motionĪn object at rest tends to remain at rest and an object in motion tends to continue moving with constant velocity unless compelled by a net external force to act otherwise.Īn object at rest tends to remain at rest and an object in rotation tends to continue rotating with constant angular velocity unless compelled by a net external torque to act otherwise.Īcceleration is directly proportional to net force and inversely proportional to mass orĪngular acceleration is directly proportional to net torque and inversely proportional to moment of inertia orįor every action there is an equal and opposite reaction. Part 1: Rotational dynamics For the diagram shown, the hanging mass is allowed to fall, thus pulling on the string and rotating the pulley.
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