A sphere with mass m=4g at the end of a massless strand is swaying in a circle o

Question

A sphere with mass m=4g at the end of a massless strand is swaying in a circle of radius R=1.51m with an angular velocity w=2rad/s.

A) Write an expression for the velocity v of the sphere.

B) Calculate the velocity of the sphere, v in m/s.

C) In order to travel in a circle, the direction the spheres path must constatly be changing (curving inwards). This constant change is direction torwards the center of the circle is the center pointing acceleration called centripetal acceleration ac. Write an expression for the centripetal acceleration ac of the sphere, in terms of linear velocity.

D) Calculate the centripetal of the sphere, ac in m/s2.

PLEASE SHOW WORK! Thanks

Explanation / Answer

Given,

m = 4 g ; R = 1.51 m ; w = 2 rad/s

A)We know that the angular and linear velocities are related as:

v = R w

B)v = R w = 1.51 x 2 = 3.02 m/s

Hence, v = 3.02 m/s

C)the centripital accleration is given by:

ac = v^2/R

D)ac = v^2/R = 3.02^2/1.51 = 6.04 m/s^2

Hence, ac = 6.04 m/s^2

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