A uniform 40-N board supports two children weighing 500 N and 350 N. If the support is at the center of the board and the 500-N
1 answer:
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Answer:
(a) k =
(b) τ = ∝
Explanation:
The moment of parallel pipe rotating about it's axis is given by the formula;
I = ---------------------------------1
(a) The kinetic energy of a parallel pipe is also given as;
k = --------------------------------2
Putting equation 1 into equation 2, we have;
k =
k =
(b) The angular momentum is given by the formula;
τ = Iw -----------------------3
Putting equation 1 into equation 3, we have
τ =
But
τ = dτ/dt = ------------------4
where
dw/dt = angular acceleration =∝
Equation 4 becomes;
τ = ∝
Answer:
0.087 m
Explanation:
Length of the rod, L = 1.5 m
Let the mass of the rod is m and d is the distance between the pivot point and the centre of mass.
time period, T = 3 s
the formula for the time period of the pendulum is given by
.... (1)
where, I is the moment of inertia of the rod about the pivot point and g is the acceleration due to gravity.
Moment of inertia of the rod about the centre of mass, Ic = mL²/12
By using the parallel axis theorem, the moment of inertia of the rod about the pivot is
I = Ic + md²
Substituting the values in equation (1)
12d² -26.84 d + 2.25 = 0
d = 2.15 m , 0.087 m
d cannot be more than L/2, so the value of d is 0.087 m.
Thus, the distance between the pivot and the centre of mass of the rod is 0.087 m.