Answer:
a = 0.1 s b. 10 s
Explanation:
Given that,
The frequency in circular motion, f = 10 Hz
(a) Let T is the period of itsrotation. We know that,
T = 1/f
So,
T = 1/10
= 0.1 s
(b) Frequency is number of rotations per unit time. So,
Hence, this is the required solution.
Answer:
(a) 0.115 m
(b) 2.08 x 10^-5 J
Explanation:
mass of bob, m = 81 g = 0.081 kg
The equation of oscillation is given by
θ = 0.068 Cos {9.2 t + Ф}
Now by comparison
The angular velocity
ω = 9.2 rad/s
(a)
where, L be the length of the pendulum
L = 0.115 m
(b) A = L Sinθ
A = 0.115 x Sin 0.068
A = 7.8 x 10^-3 m
Maximum kinetic energy
K = 0.5 x mω²A²
K = 0.5 x 0.081 x 9.2 x 9.2 x 7.8 x 7.8 x 10^-6
K = 2.08 x 10^-5 J
Answer:
w = w₀ M / (M + 2m)
Explanation:
This exercise can be solved using the concepts of conservation of angular momentum
L = I w
Let's write in angular momentum in two points
Initial. Before impact
L₀ = I w₀
Final. After the rock has stuck
= I w + (m r²) w
The system is formed by the disk and the rock, so that the forces and moments during the crash are internal and the angular momentum is preserved
L₀ =
I w₀ = (I + m r²) w
w = w₀ I / (I + m r²)
The roundabout is a disk so its moment of inertia is
I = ½ M r²
w = w₀ ½ Mr² / (½ M r² + mr²)
w = w₀ ½ M / (½ M + m)
w = w₀ ½ M2 / (M + 2m)
w = w₀ M / (M + 2m)