i have two questions: 1) in the solution for this problem, they have used kinema

Question

i have two questions:

1) in the solution for this problem, they have used kinematic eqution (for constant accelerations) to solve for the time. my question is, how do you know its constant acceleration?? they dont mention in the question that the bowling ball moves with constant acceleration, so how do we know?

2) i know since acceleration in the linear kinematic is negative(ball is slowing down), the sign for acceleration is negative, which is in the solution. but the acceleration for the rotational kinematic should also be negative, since the angular acceleration is clockwise and clockwise acceleration is negative( but the solution has positive angular acceleration), why?

A spherical bowling ball with mass m = 4.2 kg and radius R = 0.114 m is thrown down the lane with an initial speed of v = 8 7 m/s. The coefficient of kinetic friction between the sliding ball and the ground is mu = 0.32 Once the ball begins to roll without slipping it moves with a constant velocity down the lane. How long does it take the bowling ball to begin rolling without slipping? v = v0 - at Once v = omega R it rolls without slipping omega = alpha t omega R = alpha Rt v= v0 - at a = mu g alpha = 5 mu g/2 R v = omega R v0 - at = alpha tR v0 - mu gt = 5 mu g/2 t v0 = 7 mu g/2 t t = 2/7 mu g v0

Explanation / Answer

1)acceleration is constant because force of friction is constant=umg;hence acceleration is ug (constant)

2)for sphere to roll without slipping v should be equal to -rxw(here x is the cross product of vectors)

(v+wr=0,beacuse point of contact with the ground should be 0).

yes angular acceleration is anti clock wise and is negative.since, v=-wr.hence -(negative wr)is positive).

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