A pitcher throws a curveball that reaches the catcher in 0.55 s. The ball curves because it is spinning at an average angular velocity of 335 rev/min (assumed constant) on its way to the catcher's mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher to the catcher?
Is my answer correct?
disp = angular vel x time
disp = (335x360x0.1745/60)x 0.55
disp = 19.29 radians
0.55 s * 335/60 (rev/s) * 2 pi (rad/rev) => same answer. Looks good to me
Thanks!
Yes, your answer is indeed correct. To calculate the angular displacement (in radians), you can use the formula:
Angular displacement = angular velocity x time
First, convert the angular velocity from rev/min to rev/s:
335 rev/min * (1 min/60 s) = 5.58 rev/s
Then, convert rev/s to radians/s by multiplying by 2π (since there are 2π radians in one revolution):
5.58 rev/s * 2π rad/rev = 35.09 rad/s
Finally, multiply the angular velocity by the time:
35.09 rad/s * 0.55 s = 19.30 radians
So your answer of 19.29 radians is correct.
Alternatively, you can simplify the calculation by combining the conversion factors:
0.55 s * 335/60 (rev/s) * 2π (rad/rev) = 19.29 radians
Both methods yield the same result, so your answer is correct.