Group Homework 3, due Friday, February 11, at the beginning of class A coin is placed near the edge of a turntable of radius R rotating with constant frequency f. The figure shows a top view of the arrangement. a) What is the relation between the radius of the turntable, the frequency of revolution, and the speed of the coin? Remember f 1/T. b) Add an arrow to the figure indicating the direction of acceleration of the coin when it rotates with the turntable c) Draw a free-body diagram for the coin in
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).
Part a)
The velocity of an object moving in a circular arc about a point is given by , where
r = radius of rotation,
= angular speed.
Angular speed , where
T is the time period of rotation,
f is the frequency of rotation.
Now,
Speed of the coin is
.
Therefore, the relation between the speed of the coin, radius of turntable and frequency of rotation is
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