Find the following three values using just rotational kinematics.

Question

Find the following three values using just rotational kinematics.(a) A ball rolls down a $1.5$-meter long incline from rest to $3.2\,\text{m/s}$. The ball has a $16.0\,\text{cm}$ radius. Find the angular acceleration of the ball.
, (b) A CD player spins at $7329\,\text{rpm}$. It starts from rest and has an acceleration of $419\,\text{rad/s}^2$. How long does it take to reach full speed?
, (c) A rotating object has a uniform angular acceleration of $5.15\,\text{rad/s}^2$. How long does it take to speed up from $3.33\,\text{rad/s}$ to $33.3\,\text{rad/s}$?
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Jason · Accepted Answer

(a) Angular acceleration of the ball is $ \approx 21.33 \, \text{rad/s}^2 $.
(b) Time for the CD player to reach full speed is $ \approx 1.83 \, \text{s} $.
(c) Time to accelerate for the rotating object is $ \approx 5.82 \, \text{s} $.

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