A 1.5kg mass is spun on a string in a 50cm diameter circle with a constant linea

Question

A 1.5kg mass is spun on a string in a 50cm diameter circle with a constant linear velocity of 5m/s. Over the course of 2.5seconds, the is gradually shortened until it is only 5cm long. Draw an example and Find: 1.)What is the angular velocity of the mass before the string is made shorter? 2.) What is the angular velocity of the mass after the string is made shorter? 3.)What is the angular acceleration of the mass? 4.)How many revolutions will the mass make while the string being shortened? 5.)How much work must be done by the string while the string is being shortened?

Explanation / Answer

a)

we know that v=r

where is the angular velocity

v is the linear velocity and r is the radius

r=25cm or r=0.25m

so,

5=.25

=20 rad/s

b)

now the radius is shorted to 0.05 cm,

So will be

5/0.05

100 rad/s

c)

we know that angular accelrataion is

change in angular velocity/time.

So,

angular acc=(100-20)/2.5

=32rad/s2

d)

now also angular displacmnet is

=0.5t2

=0.5*32*2.52

=100rad.

in one revolution there are 2*3.14 rad,

So no of revolution is

100/6.28

=15.923

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