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A student has 65-cmlong arms. What is the minimum angular velocity (in rpm) for swinging a bucket of water in a vertical circle without spilling any? The distance from the handle to the bottom of the bucket is 35cm.

Short Answer

Expert verified

The minimum angular velocity of the bucket of water is29.9rpmor30rpm.

Step by step solution

01

Given information

Student's arm length=65cm

The distance from the handle to the bottom of the bucket=35cm

02

Angular velocity 

Angular velocity can be characterized as the pace of progress of angular dislodging.

Calculate the minimum angular velocity of the bucket of the water. The total distance from the shoulder to the bucket is,

R=65cm+35cm

localid="1649398245082" =100cm10-2m1cm

=1m

The net force on the bucket of water is,

Fnet=Fcent

Here,Fcent is the centripetal force.
mg=m2R

g=2R

Rearrange the above equation for.

03

Rearrange the equation 

Rearrange the equation for .

=gR

Substitute the values

localid="1649398261321" g=9.81m/s2

localid="1649398276295" R=1m

localid="1649398291087" =9.81m/s21m

localid="1649398301907" =3.13rad/s1rev2

=29.9rpm

30rpm

04

Final answer

The minimum angular velocity of the bucket of water is 29.9rpmor30rpm.

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