A Billiard Ball, radius 1.25 in and mass of 165 g , is released from rest and rolls down a smooth incline (like galileos ramp...) that is 8 ft long. The incline has a height of 4 in going to 0 inches in 8 ft. There I no slipping. a. How many revolutions did the ball make going down the incline? b. What was the angular acceleration of the ball? c. What was the tangential acceleration of the ball? d. What’s the difference? e. How long does it take the billiard ball to reach the bottom of the ramp? f. How fast is it traveling at the bottom of the incline? (what are the balls angular AND tangential velocity at the bottom of the ramp?) How would all this change if we used a golf ball instead? (mass 56 g radius 0.5 in)
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 Billiard Ball, radius 1.25 in and mass of 165 g , is released from rest and rolls down a smooth incline (like galileos ramp...) that is 8 ft long. The incline has a height of 4 in going to 0 inches in 8 ft. There I no slipping.
a. How many revolutions did the ball make going down the incline?
b. What was the
c. What was the tangential acceleration of the ball?
d. What’s the difference?
e. How long does it take the billiard ball to reach the bottom of the ramp?
f. How fast is it traveling at the bottom of the incline? (what are the balls angular AND tangential velocity at the bottom of the ramp?) How would all this change if we used a golf ball instead? (mass 56 g radius 0.5 in)
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