Translational Speed of a Bowling Ball

In summary, the conversation discusses the calculation of the translational speed of a bowling ball rolling down an incline. The conversation includes equations for angular velocity and moment of inertia, and the correct calculation is found to be 2/5 for the moment of inertia of a solid sphere. The final answer for the translational speed is 5.1 m/s.
  • #1
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1. A bowling ball with a mass of 6.95 kg and a radius of 0.194 m starts from rest at a height of 2.21 m and rolls down a 49.2 degree slope. What is the translational speed of the ball when it leaves the incline?


2. Unsure! Here's what I've got, though:
ω = v/r
mgh=1/2mv2+1/2Iω2
And so: ω= √(2mgh/(mr2+I))
I of a solid sphere = 2/3(m)(r2)


The Attempt at a Solution


I = 2/3(6.95)(.1942) = 0.174
ω= √(2(6.95)(9.8)(2.21)/((6.95)(.1942+0.174)) = √(301.05)/(0.436) = 26.29
v = ωr
v = 26.20 X 0.194 = 5.1
Alas, 5.1 is not the correct answer. I'm sure I need to factor in the angle somewhere, but I don't know how! Help, please!
 
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  • #2
Are you sure the moment of inertia for a solid sphere is 2/3?
I thought that was for a hollow sphere.
Try 2/5?

http://img80.imageshack.us/img80/5226/picture2hr.png
 
Last edited by a moderator:
  • #3
Oh my goodness, has this been my problem the whole time?

I tried it, it was! You are such a lifesaver, thank you so much! I couldn't for the life of me figure out what I was doing wrong! Thanks again!
 

Related to Translational Speed of a Bowling Ball

1. What is the translational speed of a bowling ball?

The translational speed of a bowling ball refers to the speed at which the ball is moving in a straight line. It is typically measured in miles per hour (mph) or meters per second (m/s).

2. How is the translational speed of a bowling ball calculated?

The translational speed of a bowling ball can be calculated by dividing the distance the ball has traveled by the time it took to travel that distance. This calculation is known as average speed and can be represented by the formula: speed = distance/time.

3. What factors affect the translational speed of a bowling ball?

Several factors can affect the translational speed of a bowling ball, including the weight and size of the ball, the amount of force applied by the bowler, and the surface of the bowling lane. Other factors such as air resistance and friction can also play a role in the speed of the ball.

4. How does the translational speed of a bowling ball impact its trajectory?

The translational speed of a bowling ball can greatly impact its trajectory. A higher speed will result in a straighter and faster trajectory, while a lower speed may cause the ball to curve or hook. The angle at which the ball is released and the amount of spin applied can also affect its trajectory.

5. Can the translational speed of a bowling ball be increased?

Yes, the translational speed of a bowling ball can be increased by applying more force during the release, adjusting the angle of release, or using a lighter ball. However, it is important to note that increasing the speed can also make it more difficult to control the ball's trajectory and accuracy.

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