Question

GENERAL PHYSICS (PHYS 2205/2206) STANDARD VIEW Your answer is partially correct Try again PRINTER VERSION BACK NEXT The drawing shows two identical systems of objects; each consists of the same three small balls connected by massless rods. In both systems the axis is perpendicular to the page, but it is located at a different place, as shown. The same force of magnitude F is applied to the same ball in each system (see the drawing). The masses of the balls are m, 9.0 kg, my - 6.1 kg, and my 7.9 kg. The magnitude of the force is F518 N. (a) For each of the two systems, determine the moment of inertia about the given axis of rotation. (b) Calculate the torque (magnitude and direction) acting on each system. (e) Both systems start from rest, and the direction of the force moves with the system and always points along the 4.00-m rod. What is the angular velocity of each system after 5.99 s? 3.00 m 3.00m Asis 4.00 m 4.00 m 5.00 m 5.00 m Ais System A System (a)-252.4 kg-m 2 t T279.9 kg-m 2 1154 N-m 2 (b) rA N-m 36.88 +t (e) aA rad/s rad/s

Answer 1

Let Moment of inertia of the system when axis is passing through m₁ be I₁

I₁= m₂$\times$ 3² + m₃$\times$ 5² = 6.1 $\times$ 9 + 7.9 $\times$ 25 = 252.4 kg m²

Let Moment of inertia of the system when axis is passing through m₃ be I₂

I₂ = m₁$\times$ 5² + m₂$\times$ 4² = 9 $\times$ 25 + 6.1 $\times$ 16 = 322.6 kg m²

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Torque
1
about axis passing through m₁ = r $\times$ F = 3 $\times$ 518 = 1554 N m

r and F are vectors and r $\times$ F is cross product of vectors.

For torque . Force vector is perpendicular to distance from point of application to axis.

1

Torque $\tau _{2}$ about axis passing through m₃ = r $\times$ F = 0 , because force vector is parallel

to distance from point of application to axis.

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Angular acceleration $\alpha$ is obtained from , $\tau = I\times \alpha$

for the system-1, angular acceleration $\alpha$ = 1554/ 252.4 = 6.16 rad/s

angular velocity $\omega$ after 5.99s = $\alpha$ t = 6.16*5.99 = 36.9 rad /s

for system-2, $\tau _{2}$ = 0 , hence angular acceleration and angular velocity are zero

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