Answer:
0.893 rad/s in the clockwise direction
Explanation:
From the law of conservation of angular momentum,
angular momentum before impact = angular momentum after impact
L₁ = L₂
L₁ = angular momentum of bullet = + 9 kgm²/s (it is positive since the bullet tends to rotate in a clockwise direction from left to right)
L₂ = angular momentum of cylinder and angular momentum of bullet after collision.
L₂ = (I₁ + I₂)ω where I₁ = rotational inertia of cylinder = 1/2MR² where M = mass of cylinder = 5 kg and R = radius of cylinder = 2 m, I₂ = rotational inertia of bullet about axis of cylinder after collision = mR² where m = mass of bullet = 0.02 kg and R = radius of cylinder = 2m and ω = angular velocity of system after collision
So,
L₁ = L₂
L₁ = (I₁ + I₂)ω
ω = L₁/(I₁ + I₂)
ω = L₁/(1/2MR² + mR²)
ω = L₁/(1/2M + m)R²
substituting the values of the variables into the equation, we have
ω = L₁/(1/2M + m)R²
ω = + 9 kgm²/s/(1/2 × 5 kg + 0.02 kg)(2 m)²
ω = + 9 kgm²/s/(2.5 kg + 0.02 kg)(4 m²)
ω = + 9 kgm²/s/(2.52 kg)(4 m²)
ω = +9 kgm²/s/10.08 kgm²
ω = + 0.893 rad/s
The angular velocity of the cylinder bullet system is 0.893 rad/s in the clockwise direction-since it is positive.
Dispersion occurs due to the different degrees of refraction experienced by different colours of light. Light of different colours may travel with the same speed in a vacuum, but they travel at different speeds in some refracting medium. The speed of violet light is relatively lower than that of red light.
Answer:
0.2 J
Explanation:
The pendulum forms a right triangle, with hypotenuse of 50 cm and base of 30 cm. The height of this triangle can be found with Pythagorean theorem:
c² = a² + b²
(50 cm)² = a² + (30 cm)²
a = 40 cm
The height of the triangle is 40 cm. The height of the pendulum when it is at the bottom is 50 cm. So the end of the pendulum is lifted by 10 cm. Assuming the mass is concentrated at the end of the pendulum, the potential energy is:
PE = mgh
PE = (0.200 kg) (9.8 N/kg) (0.10 m)
PE = 0.196 J
Rounding to one significant figure, the potential energy is 0.2 J.
