# A wheel of diameter 0.45m starts from rest and rotates with uniform acceleration to 6000rpm (rev/min) in a time of 4s. Find the speed of a point on the rim at the end of 4s. Show your work. Many...

A wheel of diameter 0.45m starts from rest and rotates with uniform acceleration to 6000rpm (rev/min) in a time of 4s. Find the speed of a point on the rim at the end of 4s. Show your work.

Many thanks.

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### 1 Answer

Given rotation perminute=6000

In 1 min . wheel revolves 6000

In 60 sec. wheel revolution=6000

In 1 sec. its revolution will be= 6000/60

=100

Given diameter of the wheel = .45 m

Thus radius will be= .45/2

So angular velocity = 100 rev/sec

so linear velocity = rw

=(.45/2)xx100

=22.5 m/s

u=initial velocity =0 m/s

v=velocity after 1 sec= 22.5 m/s

because there is uniform acceleration

a= (v-u)/t

=(22.5-0)/1

=22.5ms^(-2)

Thus velocity after 4 sec. will be v say, then we can calculate it by following

v=u+at

v=0+(22.5)x4

v=90 m/s

Thus velocity of the point on the rim after 4 sec= 90 m/sec.