Consider a bowling ball which is tossed down a bowling alley. For this problem, we will consider the bowling ball to be a uniform sphere of mass M and radius R, with a moment of inertia given by I = (2/5)MR2. The moment the ball hits the ground (t = 0), it is moving horizontally with initial linear speed v0, but not rotating (ω0 = 0). Due to kinetic friction between the ground and the ball, it begins to rotate as it slides. The coefficient of kinetic friction is µk. As the ball slides along the lane, its angular speed steadily increases. At some point (time tc), the “no-slip” condition kicks in, so that ω = v/R. After this, the ball moves with a constant linear and angular speed. Solve all parts of this problem symbolically. Use the rotational version of Newton’s second law to find an expression for the angular acceleration of the ball along the z-direction before the no-slip condition kicks in, αz. Your final expression should only involve the variables R, g, and µ
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).
Consider a bowling ball which is tossed down a bowling alley. For this problem, we will consider the bowling ball to be a uniform sphere of mass M and radius R, with a moment of inertia given by I = (2/5)MR2. The moment the ball hits the ground (t = 0), it is moving horizontally with initial linear speed v0, but not rotating (ω0 = 0). Due to kinetic friction between the ground and the ball, it begins to rotate as it slides. The coefficient of kinetic friction is µk. As the ball slides along the lane, its angular speed steadily increases. At some point (time tc), the “no-slip” condition kicks in, so that ω = v/R. After this, the ball moves with a constant linear and angular speed. Solve all parts of this problem symbolically.
Use the rotational version of Newton’s second law to find an expression for the
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