Please show all steps. 1. A child rolls a ball on a level floor 6.7 m to another

Question

Please show all steps.

1.

A child rolls a ball on a level floor 6.7 m to another child. If the ball makes 14.0 revolutions, what is its diameter?

2.

A 36-cm-diameter wheel accelerates uniformly about its center from 150 rpm to 340 rpm in 3.8 s

PART A: Determine its angular acceleration.

PART B : Determine the radial component of the linear acceleration of a point on the edge of the wheel 1.9 s after it has started accelerating.

PART C: Determine the tangential component of the linear acceleration of a point on the edge of the wheel 1.9 s after it has started accelerating.

3.

A centrifuge rotor has a moment of inertia of 5.50×102 kgm2 . How much energy is required to bring it from rest to 9480 rpm ?

Explanation / Answer

1)
Let r is the radius of the ball.

distance travelled, L = N*2*pi*r

r = L/(N*2*pi)

= 6.7/(14*2*pi)

= 0.076 m

so, diameter, d = 2*r

= 2*0.076

= 0.152 m or 15.2 cm

2)

A)
w1 = 150 rpm

w2 = 340 rpm

angular acceleration, alfa = (w2 - w1)/t

= (340 - 150)/3.8

= 50 rev/s^2

= 50*2*pi rad/s^2

= 314 rad/s^2

B) radius, r = d/2

= 36/2

= 18 cm

= 0.18 m

angular speed, at time t = 1.9s

w = w1 + alfa*t

= 150 + 50*1.9

= 245 rpm

= 245*2*pi/60

= 25.64 rad/s

a_rad = r*w^2

= 0.18*25.64^2

= 118.4 m/s^2

C) a_tan = r*alfa

= 0.18*314

= 56.52 m/s^2

3)

w1 = 0

w2 = 9480 rpm = 9480*2*pi/60 = 992.74 rad/s

Energy required = 0.5*I*(w2^2 - w1^2)

= 0.5*5.5*10^-2*(992.74^2 - 0^2)

= 27102 J

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