2. A solid cylinder of mass M and radius R starts from rest and rolls without sl

Q: 2. A solid cylinder of mass M and radius R starts from rest and rolls without sl

3) let the final speed at the centre of mass is v for rolling with out slipping v = r*w Now , Using conservation of energy 0.5 * I * w^2 + 0.5 * m v^2 = mg * h 0.5 * 0.5 * m * r^2 *(v/w)^2 + 0.5 * mv^2 = mgh 0.75 * v^2 = gh v = sqrt(1.33 * gh) the velocity of centre of mass is sqrt(1.33 * gh)

ID: 1395257 • Letter: 2

Question

2. A solid cylinder of mass M and radius R starts from rest and rolls without slipping down an inclined plane of length L and height h. Find the speed of its center of mass when the cylinder reaches the bottom of the inclined plane. 3. Suppose that the Sun runs out of nuclear fuel and suddenly collapses to form a so-called white dwarf star, with a diameter equal to that of earth. Assuming no mass loss, what would then be the new rotation period of the Sun, which currently is about 25 days? Assume that the Sun and the white dwarf are uniform spheres.

Explanation / Answer

let the final speed at the centre of mass is v

for rolling with out slipping

v = r*w

Now , Using conservation of energy

0.5 * I * w^2 + 0.5 * m v^2 = mg * h

0.5 * 0.5 * m * r^2 *(v/w)^2 + 0.5 * mv^2 = mgh

0.75 * v^2 = gh

v = sqrt(1.33 * gh)

the velocity of centre of mass is sqrt(1.33 * gh)

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2. A solid cylinder of mass M and radius R starts from rest and rolls without sl

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