In ander for an object to rull smoothly (with constant angular acceleration) down a ramp, i must have either spherical or gylindrical symmetry. Consider spherically and cylindrically symmatric objects with mass M and outer radius Rrolling without slipping down an incline of height h and angle e frum the horiscntal. The rotational inertias of such objects can be writtem in the gemralined form: I- cMR", uhere cis a shape factor whose valae depemds on the geometry of the object. (f yeu lock at thr lable of rotational inertim in ther testhoek you'l be able to se that thin in trac) (For this questim, cmider M. Rk, md ga the gin quantities -apres ger amers in er of me all of these guantition. Sinplijy yoar ara a ack an you can.) If the object starts from sest at the very top of the ramp before rolling frvely down the ramp without slipping, find the object's (linear) rotational speed at the botom of the ramp. (Hint ase caseration of emergg

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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).