Bowling ball rolling - velocity, acceleration, time

AI Thread Summary
A bowler throws a bowling ball with an initial speed of 8.10 m/s and no spin, experiencing kinetic friction that causes both linear and angular acceleration. The linear acceleration is calculated as 1.86 m/s², and the angular acceleration is 42.3 rad/s². The discussion focuses on deriving the equations needed to determine the time and distance the ball slides before it begins to roll smoothly without slipping. Key equations include v = at for linear motion and ω = αt for angular motion, with the condition for rolling established as v = rω. The participants seek clarification on these equations and their application in solving the problem.
mybrohshi5
Messages
365
Reaction score
0

Homework Statement



A bowler throws a bowling ball of radius 11.0 cm along a lane. The ball slides on the lane with an initial speed of 8.10 m/s and an initial angular speed of zero (i.e. the ball is not spinning at all when it first makes contact with the lane). The coefficient of kinetic friction between the ball and the lane is 0.19.
The kinetic frictional force f_k acting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of the ball. When the center-of-mass speed V_cm has decreased enough and the spin rate has increased enough, the ball stops sliding and begins to roll smoothly without slipping.

A) For what length of time does the ball slide?
B) Over what distance does the ball slide?
C) What is the linear speed of the ball when smooth rolling begins?


The Attempt at a Solution



I am having trouble coming up with the equations to solve for these.

I found the linear acceleration of the ball from an earlier part a = 1.86 m/s^2

I also found the angular acceleration of the ball from an earlier part \alpha = 42.3 rad/s2

I know i need 3 equations and they will have three unknowns.

This is what i have came up with

V = a*t

\omega = \alpha*t

Are these two right for what i am trying to find? And any help on finding a third equation would be greatly appreciated :)

Thank you
 
Physics news on Phys.org
Hi mybrohshi5! :smile:

(have an omega: ω and an alpha: α and try using the X2 tag just above the Reply box :wink:)
mybrohshi5 said:
A) For what length of time does the ball slide?
B) Over what distance does the ball slide?
C) What is the linear speed of the ball when smooth rolling begins?[/B]

As you know, the speed of the centre of mass depends only on the (net) force, and the angular acceleration about the centre of mass depends only on the torque about the centre of mass …

now use the definition of rolling, that it happens (ie sliding stops) when v = aω. :smile:
 
I am a little confused about your explanation and where v=aω comes from? the only equations i have seen dealing with angular velocity and accel are

t = Iα
v = rω

and various alternations of those of course :)
 
oops!

mybrohshi5 said:
I am a little confused about your explanation and where v=aω comes from?

oops! :redface:

sorry, i meant v = rω. :blushing:
 
Oh ok thank you. Were my first two equations the right ones to use for this type of problem?

v = at
ω = αt

t being time

Thank you for the help :)
 
Last edited:
Yup! … you use F = ma with v = at,

and τ = iα with ω = αt. :smile:
 
Perfect Thank you very much tiny-tim
 
Back
Top