Answer:

Explanation:
It is given that,
Diameter of cylinder, d = 6.6 cm
Radius of cylinder, r = 3.3 cm = 0.033 m
Acceleration of the string, 
Displacement, d = 1.3 m
The angular acceleration is given by :



The angular displacement is given by :



Using the third equation of rotational kinematics as :

Here, 



Since, 1 rad/s = 9.54 rpm
So,

So, the angular speed of the cylinder is 571.42 rpm. Hence, this is the required solution.
Answer:
horizontal component of normal force is equal to the centripetal force on the car
Explanation:
As the car is moving with uniform speed in circle then the force required to move in the circle is towards the center of the circle
This force is due to friction force when car is moving in circle with uniform speed
Now it is given that car is moving on the ice surface such that the friction force is zero now
so here we can say that centripetal force is due to component of the normal force which is due to banked road
Now we have


so we have

so this is horizontal component of normal force is equal to the centripetal force on the car
Complete Question
A gas gun uses high pressure gas tp accelerate projectile through the gun barrel.
If the acceleration of the projective is : a = c/s m/s2
Where c is a constant that depends on the initial gas pressure behind the projectile. The initial position of the projectile is s= 1.5m and the projectile is initially at rest. The projectile accelerates until it reaches the end of the barrel at s=3m. What is the value of the constant c such that the projectile leaves the barrel with velocity of 200m/s?
Answer:
The value of the constant is 
Explanation:
From the question we are told that
The acceleration is 
The initial position of the projectile is s= 1.5m
The final position of the projectile is 
The velocity is 
Generally 
and acceleration is 
so

=> 

integrating both sides

Now for the limit
a = 200 m/s
b = 0 m/s
c = s= 3 m
d =
= 1.5 m
So we have

![[\frac{v^2}{2} ] \left | 200} \atop {0}} \right. = c [ln s]\left | 3} \atop {1.5}} \right.](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bv%5E2%7D%7B2%7D%20%5D%20%5Cleft%20%7C%20200%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.%20%20%3D%20c%20%5Bln%20s%5D%5Cleft%20%7C%203%7D%20%5Catop%20%7B1.5%7D%7D%20%5Cright.)
![\frac{200^2}{2} = c ln[\frac{3}{1.5} ]](https://tex.z-dn.net/?f=%5Cfrac%7B200%5E2%7D%7B2%7D%20%20%3D%20%20c%20ln%5B%5Cfrac%7B3%7D%7B1.5%7D%20%5D)
=> 

... the density of the liquid
... the volume of the submerged object