Answer:
(a) 0.426 rad/s
(b) Before 296.225 J and After 148.5 J
Explanation:
At the center of merry-go-round, the person's weight is 75 Kg with moment of inertia of 820 kgm2 and the initial angular velocity is 0.85 rad/s
At the edge, the new angular velocity gained depends on the new moment of inertia
Here, the final moment of inertia is given by Initial moment of inertia + 
where M is the mass and R is the radius of merry-go-round
Final moment of inertia=
From the law of conservation of angular momentum as torque is zero
and making 
the subject then
where 
and 
are initial and final moment of inertia, 
and are initial and final angular velocity.
Substituting the provided values
(b)
Initial rotational kinetic energy is given by
The final rotational kinetic energy is given by
C. A complete revolution is 360 degree. two revolution is 720.
Answer:
Explanation:
Since energy is conserved:
2
mu
2
=
2
mv
2
+mgh
⇒u
2
=v
2
+2gh
⇒(3)
2
=v
2
+2(9.8)(0.5−0.5cos60)
⇒v=2m/s
Answer:
3.76 m/s
Explanation:
Instantaneous velocity: This can be defined as the velocity of an object in a non uniform motion. The S.I unit is m/s.
v' = dx(t)/dt..................... Equation 1
Where v' = instantaneous velocity, x = distance, t = time.
Given the expression,
x(t) = 28.0 m + (12.4 m/s)t - (0.0450 m/s³)t³
x(t) = 28 + 12.4t - 0.0450t³
Differentiating x(t) with respect to t.
dx(t)/dt = 12.4 - 0.135t²
dx(t)/dt = 12.4 - 0.135t²
When t = 8.00 s.
dx(t)/dt = 12.4 - 0.135(8)²
dx(t)/dt = 12.4 - 8.64
dx(t)/dt = 3.76 m/s.
Therefore,
v' = 3.76 m/s.
Hence, the instantaneous velocity = 3.76 m/s
Sound is an example of a mechanical wave. Mechanical waves are the kinds of waves that cannot be propagated without a medium. As such, these waves cannot travel through a vacuum, just like how sound cannot travel through space, since space is a vacuum.
