A uniform wooden meter stick has a mass of m = 7.49 g. A clamp can be attached t

Question

A uniform wooden meter stick has a mass of m = 7.49 g. A clamp can be attached to the measuring stick at any point so that it can freely pivot around point P, which is a distance d from the zero-end of the stick as shown. Randomized Variables m = 749 g Part (a) Calculate the moment of inertia in kgmiddotm^2 of the meter stick if the pivol point P is at the 50-cm mark. Numeric: A numeric value is expected and not an expression. I_a = Part (b) Calculate the moment of inertia in kgmiddotm^2 of the meter stick if the pivot point P is at the 0-cm mark d = 0 cm. Numeric: A numeric value is expected and not an expression. I_b = Part (c) Calculate the moment of inertia in kgmiddotm^2 of the meter stick if the pivot point P is at the d = 25 cm mark. Numeric: A numeric value is expected and not an expression. I_c = Part (d) Calculate the moment of inertia in kgmiddotm^2 of the meter stick if the pivot point P is at the d = 63 cm mark. Numeric: A numeric value is expected and not an expression. I_d = Part (c) Determine a general expression for the moment of inertia of a meter stick I_e of mass m in kilograms pivoted abeut point P, any distance d in meters from the zero-cm mark. Expression: I_e = Select from the v ariables below to write your expression. Note that all variables may not be required. alpha, beta, theta, a, b, c, d, g, h, j, k, m, P, S, t Part (f) The meter stick is now replaced with a uniform yard stick with the same mass of m = 749 g. Calculate the moment of inertia in kgmiddotm^2 of the yard stick if the pivot point P is at the 50-cm mark. Numeric: A numeric value is expected and not an expression. I_f =

Explanation / Answer

a)

m =mass of meter stick = 749 g = 0.749 kg

L = length = 1 m

at r = L/2 = center of mass

Moment of inertia is given as

Ic = mL2/12 = (0.749) (1)2/12 = 0.062 kgm2

b)

at r = 0 cm

Moment of inertia at one end is given as

I = mL2/3 = (0.749) (1)2/3 = 0.25 kgm2

c)

d = distance from center of mass = 50 cm - 25 cm = 25 cm = 0.25 m

Ip = Ic + md2

Ip = 0.062 + (0.749) (0.25)2 = 0.11 kgm2

d)

d = distance from center of mass = 63 cm - 50 cm = 13 cm = 0.13 m

Ip = Ic + md2

Ip = 0.062 + (0.749) (0.13)2 = 0.075 kgm2

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