Four objects are held in position at the corners of a rectangle by light rods as

Question

Four objects are held in position at the corners of a rectangle by light rods as shown in the figure below. (The mass values are given in the table.) m1 (kg) m2 (kg) m3 (kg) ma (kg) 1.9 4.30 3.30 2.10 6.00 m 1m 4.00 m- (a) Find the moment of inertia of the system about the x-axis. kg m2 (b) Find the moment of inertia of the system about the y-axis. kg m2 (c) Find the moment of inertia of the system about an axis through O and perpendicular to the page. Need Help? .han..i -13 points SerCP11 8.P043 My Notes Ask Your Teach odel airplane with a mass of 0.751 kg is tethered by wire so that it flies in a circle 29.5 m in radius. The airplane engine provides a net thrust of 0.803 N perpendicular to the tethering w (a) Find the torque the net thrust produces about the center of the circle. N·m (b) Find the angular acceleration of the airplane when it is in level flight rad/s2 (c) Find the linear acceleration of the airplane tangent to its flight path. m/s2 Need Help?

Explanation / Answer

2)  a) T = F x perp. distance
T = 0.803N x 29.5m ... T = 23.69 Nm

b) apply F = m x a in angular form
T = I x (/t)
( /t) = T/I
I = moment of inertia = mr² =0.751 x 29.5² =653.56 kgm²
(/t) = T/I = 23.69/653.56 .......... .... (/t) = 0.036 rad/s²

c) F= m x a
a = 0.803N /0.751kg .......... a = 1.069 m/s²

It is easier to get (/t) from (c) rather than T = I x (/t)
v = r
v/t = a = r /t .... /t = a/r = 1.069/29.5 = 0.036 rad/s²

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