Answer:
Explanation:
Velocity of Top most point of wheel is twice the Velocity of centre of mass of wheel

Thus angular velocity is given by



![K.E.=\frac{1}{2}m_{stone}V^2+2\left [ \frac{1}{2}m_{cyl}\left [ \frac{V}{2}\right ]^2\right ]+2\left [ \frac{1}{2}I\omega ^2\right ]](https://tex.z-dn.net/?f=K.E.%3D%5Cfrac%7B1%7D%7B2%7Dm_%7Bstone%7DV%5E2%2B2%5Cleft%20%5B%20%5Cfrac%7B1%7D%7B2%7Dm_%7Bcyl%7D%5Cleft%20%5B%20%5Cfrac%7BV%7D%7B2%7D%5Cright%20%5D%5E2%5Cright%20%5D%2B2%5Cleft%20%5B%20%5Cfrac%7B1%7D%7B2%7DI%5Comega%20%5E2%5Cright%20%5D)
![K.E.=\frac{V^2}{2}\left [ m_{stone}+\frac{m_{roller}}{2}\right ]+I\omega ^2](https://tex.z-dn.net/?f=K.E.%3D%5Cfrac%7BV%5E2%7D%7B2%7D%5Cleft%20%5B%20m_%7Bstone%7D%2B%5Cfrac%7Bm_%7Broller%7D%7D%7B2%7D%5Cright%20%5D%2BI%5Comega%20%5E2)
![K.E.=\frac{0.319^2}{2}\left [ 672+\frac{82}{2}\right ]+\frac{82\times 0.343^2\times 0.465^2}{2}](https://tex.z-dn.net/?f=K.E.%3D%5Cfrac%7B0.319%5E2%7D%7B2%7D%5Cleft%20%5B%20672%2B%5Cfrac%7B82%7D%7B2%7D%5Cright%20%5D%2B%5Cfrac%7B82%5Ctimes%200.343%5E2%5Ctimes%200.465%5E2%7D%7B2%7D)

Answer:
The rate of change of an object's velocity is called acceleration.
Answer:
a)
Nm⁻¹
b)
Hz
c)
ms⁻¹
d)
m
e)
ms⁻²
f)
m
Explanation:
a)
= force required to hold the object at rest connected with stretched spring = 27 N
= stretch in the spring from equilibrium position = 0.2 m
= force constant of the spring
force required to hold the object at rest is same as the spring force , hence


inserting the values
Nm⁻¹
b)
frequency of the oscillations is given as

inserting the values
Hz
c)
= Amplitude of oscillations = 0.2 m
= angular frequency
Angular frequency is given as
rads⁻¹
Maximum speed of oscillation is given as

ms⁻¹
d)
maximum speed of the object occurs at the equilibrium position, hence
m
e)
Maximum acceleration of oscillation is given as

ms⁻²
f)
maximum acceleration occurs when the object is at extreme positions, hence
m