Last summer i went to barrier island.
hope this help
Answer:
Explanation:
for rolling motion down the plane acceleration is given by the following expression
a = g sinθ / (1 + k² / R²)
here k is radius of gyration and R is radius of the object rolling down .
for cylinder I = 1/2 m R²
so k² = R² / 2
k² / R² = 1/2
a = g sinθ /( 1 + 1 / 2 )
= 2 / 3 x g sinθ
v = √ 2 a s
= √ (2 x 2 / 3 x g sinθ s )
= √ (4 / 3 x g h )
= √ (4 / 3 x g x .5 )
= √ 2g / 3
for sphere I = 2/5 m R²
so k² = 2/5 R²
k² / R² = 2 / 5
a = g sinθ / (1 + 2 / 5)
= 5 / 7 x g sinθ
v = √ 2 a s
= √ (2 x 5 / 7 x g sinθ s )
= √ (10/7 x g h )
Given
√ (10/7 x g h ) = √ 2g / 3
10/7 x g h = 2g / 3
h = 14 / 30 m
= .47 m .
Answer:
18.75 rad/s
Explanation:
Moment of inertia of the disk;
I_d = ½ × m_disk × r²
I_d = ½ × 10 × 4²
I_d = 80 kg.m²
I_package = m_pack × r²
Now,it's at 2m from the centre, thus;
I_package = 5 × 2²
I_package = 20 Kg.m²
From conservation of momentum;
(I_disk + I_package)ω1 = I_disk × ω2
Where ω1 = 15 rad/s and ω2 is the unknown angular velocity of the disk/package system.
Thus;
Plugging in the relevant values, we obtain;
(80 + 20)15 = 80 × ω2
1500 = 80ω2
ω2 = 1500/80
ω2 = 18.75 rad/s
Momentum is Mass × Velocity
= 1875×22 = 41250 kg m/sec