A hollow ball of mass Mand radius Ris released from rest at the top of a bumpy track. The starting point is at height Hfrom the bottom and the top of the bump is at height 2H/3from the bottom of the track, as shown in Fig.1.Over the entire course of its motion, the ball rolls without slipping.The acceleration due to gravity has magnitude g and air resistance is negligible. a)Explain which physical quantity (ies) is (are) conserved over the course of the displacement of the ball along the track. b) Determine the linear speed of the ball at the lowest point on the track. c) Determine which fraction of the mechanical energy of the ball its rotational kinetic energy represents when it reaches the top of the bump.
Angular speed, acceleration and displacement
Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.
Angular Position
Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.
A hollow ball of mass Mand radius Ris released from rest at the top of a bumpy track. The starting point is at height Hfrom the bottom and the top of the bump is at height 2H/3from the bottom of the track, as shown in Fig.1.Over the entire course of its motion, the ball rolls without slipping.The acceleration due to gravity has magnitude g and air resistance is negligible.
a)Explain which physical quantity (ies) is (are) conserved over the course of the displacement of the ball along the track.
b) Determine the linear speed of the ball at the lowest point on the track.
c) Determine which fraction of the mechanical energy of the ball its rotational kinetic energy represents when it reaches the top of the bump.
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