Physics HW Question - Please Take a Look?
A basketball player is balancing a spinning basketball on the tip of his finger. The angular velocity of the ball slows down from 19.0 to 14.2 rad/s. During the slow down, the angular displacement is 84.5 rad. Determine the time it takes for the ball to slow down.
If you could please let me know what the answer is and how you came up with it I would appreciate it. Thank you
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Verified answer
The equations for constant angular acceleration are exactly analogous to linear acceleration. You've been given an initial velocity, a final velocity, and a displacement. If these were linear quantities, you could do this:
vf^2 = vi^2 + 2ad: Everything here is known except a, so you can solve for it.
d = vi*t + (1/2)at^2. Everything here is known except t, so you can solve for it. It's a quadratic equation, so you need to use the quadratic formula.
Analogous equations you need to use here, replace d by theta (angle in radians), v by w (angular velocity in rad/sec), a by alpha (angular acceleration in rad/sec^2).
wf^2 = wi^2 + 2alpha*theta
theta = wi*t + (1/2)alpha*t^2
F internet appearing on the sled = F - uk*mg => accelaration of the sled = F/m - ukg => for const. Acc . V vs t curve is linear, V = at => for linear purposes avg fee is in simple terms arithmetic advise i.e intial vel + very final vel/2.