Final answer:
To calculate the centripetal acceleration of the laces on a football thrown in a spiral by Cam Newton, the angular velocity is first converted to rad/s, and then the centripetal acceleration formula is applied. The acceleration is found to be approximately 34.0 m/s².
Step-by-step explanation:
The question asks to calculate the centripetal acceleration of the laces on a football thrown in a spiral. Cam Newton throws the football at a rate of 8.0 revolutions per second (rev/s), and the radius of the football is given as 8.5 cm.
To find the centripetal acceleration, we first need to convert the angular velocity from rev/s to radians per second (rad/s) since 1 rev = 2π rad. Therefore, the angular velocity (ω) is 8.0 rev/s × 2π rad/rev = 16π rad/s.
Next, we use the formula for centripetal acceleration, ac = ω2 × r, where r is the radius of the circular path.
Converting 8.5 cm to meters (0.085 m), we get ac = (16π rad/s)2 × 0.085 m = 108.8π2 m/s². When calculated, this gives a centripetal acceleration of approximately 34.0 m/s², which corresponds to option (a).