Final answer:
The tack's tangential speed is 4.37 m/s, and its radial acceleration is 59.5 m/s². This is calculated using angular velocity and the radius of the tack's circular path.
Step-by-step explanation:
The tack’s tangential speed (v) is calculated by knowing it completes 2.17 revolutions per second and is located 32.1 cm from the rotation axis. To find the tangential speed, we convert revolutions per second to radians per second (angular velocity), since 1 revolution = 2π radians, then multiply by the radius (r).
Angular velocity, ω = 2.17 rev/s × 2π rad/rev = 13.63 rad/s
Tangential speed, v = rω = 0.321 m × 13.63 rad/s = 4.37 m/s
The tack’s radial acceleration (ar) occurs as a result of the change in the direction of the velocity of an object moving in a circular path. It can be calculated using the formula ar = ω2 × r.
Radial acceleration, ar = ω2 × r = (13.63 rad/s)2 × 0.321 m = 59.5 m/s2