1. a pariticle of mass m and speed v collides and sticks to the end of a uniform

Question

1. a pariticle of mass m and speed v collides and sticks to the end of a uniform solid cylinder of mass M and radius R. If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity of the system after the collision?

answer is 2mv/2mR+MR

2.a force of 15N acts at the end os a 2 meter uniform rod that is pivoted about its center of mass. The rod starts from rest and attains an agular velocity of 10 rad/s in 2 seconds. what is the moment of inertiaof the rod?

answer is 3 rad/s

3. a cylinder of mass M and radius R, whose moment of inertia about its center is 1/2MR^2, rolls without slipping along a level surface at speed v. The maximum vertical height to which it can roll if it ascends an incline is ....

answer is 3v^2/4g

show the work to get to the right answer please

Explanation / Answer

1. by princle of conservastion of momentum

initial momentum= final momentum

mvR= (I + m)w

I=MR^2

PUTTING the values give

w= 2mv/(2mR+ MR)

2.torque provided by force= moment of inertia* angular accn

15*2= I*5

I= 6 kg-m^2

3.

energy conservation principle

gain in potential energy = kinetic energy lost

Mgh= 1/2 Mv^2 + 1/2 Iw^2

I=1/2 MR^2

w=v/R

putting all and solving gives

Mgh= 3/4Mv^2

h= 3*v^2/4g

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