Classical mechanics questions

[Nylex]

I just want to check if my answers for these are right so far.

"Consider a ball of mass M and radius R being bowled in a bowling alley. The ball is released with velocity v0. As it makes contact with the wooden floor (of coefficient of friction, μ), the ball slows down and begins to rotate. It is both sliding and rotating."

Write down expressions for:

i. the linear deceleration

Frictional force, F = -μN = -μMg

N II: -uMg = Ma

=> a = -μg

ii. the angular acceleration

Not sure here

α = a/R, but a is -ve, which would mean α is negative :/

iii. the speed of the centre of the ball after time t

v = u + at

v = v0 - μgt

Not quite sure about this one either, cos it's worth 2 marks :/

Thanks.

[arildno]

ii) is completely incorrect; that formula relates TANGENTIAL acceleration at the rim of a fixed rotating with the angular acceleration.

What you need to do is:
Find the torque produced by the force of friction with respect to the center.
The angular acceleration is then found by the ratio between the torque and the moment of inertia.

[Nylex]

Lol, ok. Thanks. What about the others?

[arildno]

They look fine.

[Nylex]

Cheers :).

[arildno]

Note however, that in iii), the force of friction will STOP acting on some T (when the ball starts only to roll, not sliding).

Hence, in order to gain full marks here, you must determine T; after that, the centre of the ball moves with CONSTANT velocity

[Nylex]

Note however, that in iii), the force of friction will STOP acting on some T (when the ball starts only to roll, not sliding).

Hence, in order to gain full marks here, you must determine T; after that, the centre of the ball moves with CONSTANT velocity

Yeah, that's for the next part of the question.