A solid sphere is released from height h from the top of an incline making an angle θwith the horizontal. Calculate the speed of the sphere when it reaches the bottom ofthe incline (a) in the case that it rolls without slipping and (b) in the case that it slidesfrictionlessly without rolling. (c) Compare the time intervals required to reach thebottom in cases (a) and (b).
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 solid sphere is released from height h from the top of an incline making an angle θ
with the horizontal. Calculate the speed of the sphere when it reaches the bottom of
the incline (a) in the case that it rolls without slipping and (b) in the case that it slides
frictionlessly without rolling. (c) Compare the time intervals required to reach the
bottom in cases (a) and (b).
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