Jeff of the Jungle swings on a vine that is 7.20 m long. At the bottom of the sw
ID: 1457110 • Letter: J
Question
Jeff of the Jungle swings on a vine that is 7.20 m long. At the bottom of the swing, just before hitting the tree, Jeff's linear speed is 8.50 m/s. Suppose that at some point in his swing Jeff of the Jungle has an angular speed of 0.750 rad/s and an angular acceleration of 0.700 rad/s2.
A) Find the magnitude of his centripetal acceleration.
B) Find the magnitude of his tangential acceleration.
C) Find the magnitude of his total acceleration.
D) Find the angle his total acceleration makes with respect to the tangential direction of motion.
Explanation / Answer
A) a_cetripetal = r*w^2
= 7.2*0.75^2
= 4.05 m/s^2
B) a_tan = r*alfa
= 7.2*0.7
= 5.04 m/s^2
c) a_total = sqrt(a_tan^2 + a_rad^2)
= sqrt(4.05^2 + 5.04^2)
= 6.47 m/s^2
d) angle made by total acceleration with the tangetial direction,
theta = tan^-1(a_rad/a_tan)
= tan^-1(4.05/5.04)
= 38.8 degrees
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