A rod of mass M and length L is attached to a wall with a pin joint, around which the rod is free to rotate. A horizontal rope attached to the end of the rod holds the rod at an angle θo to the horizontal. Express your answer in terms of M, L, θo, and g (and no other variables). What is the tension in the rope? Suddenly the rope breaks. As a result, the rod swings down. Immediately after the rope breaks, what is the rod’s angular acceleration?
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).
A rod of mass M and length L is attached to a wall with a pin joint, around which the rod is free to rotate. A horizontal rope attached to the end of the rod holds the rod at an angle θo to the horizontal. Express your answer in terms of M, L, θo, and g (and no other variables).
- What is the tension in the rope?
- Suddenly the rope breaks. As a result, the rod swings down. Immediately after the rope breaks, what is the rod’s
angular acceleration ?
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