A disk starts to rotate about a fixed axis from rest with a certain constant angular acceleration until time t1, then it keeps rotating with a constant angular speed until time t2, finally it is brought back to rest at time t3 applying another constant angular acceleration. If we decided to graph the angular position of any point on the disk as a function of time for this situation and the rotation begins in the negative direction of rotation, we would obtain that a) From 0 seconds to t1 a linear trend with a negative slope, from t1 up to t2 a constant linear trend and from t2 to t3 a linear trend with a positive slope. b) From 0 seconds to t1 a concave quadratic trend downwards, from t1 to t2 a linear trend with a negative slope and from t2 to t3 a concave quadratic trend upwards. c) From 0 seconds to t1 a linear trend with a positive slope, from t1 to t2 a constant linear trend, and from t2 to t3 a linear trend with a negative slope. d) From 0 seconds to t1 a concave quadratic trend upward, from t1 to t2 a linear trend with a positive slope and from t2 to t3 a concave quadratic trend downward.
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).
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