A solid uniform disk of mass 55.0 kg and radius 0.25m rolls down a ramp of lengt

Question

A solid uniform disk of mass 55.0 kg and radius 0.25m rolls down a ramp of length 4.5m that make an angle of 15 degreeswitht the horizontal.

(a) Find the linear and angular speeds of the solid disk when it reaches the bottom of the ramp.

(b) If a solid sphere of the same mass and radius starts to roll down the ramp along witht he solid disk, which one will reach the bottom first.

(c) If the solid diskin part (a) is instead slipping down the slope without rolling, what is the linear speed of the disk when it reaches the bottom of the ramp

A solid uniform disk of mass 55.0 kg and radius 0.25m rolls down a ramp of length 4.5m that make an angle of 15 degreeswitht the horizontal. (a) Find the linear and angular speeds of the solid disk when it reaches the bottom of the ramp. (b) If a solid sphere of the same mass and radius starts to roll down the ramp along witht he solid disk, which one will reach the bottom first. (c) If the solid diskin part (a) is instead slipping down the slope without rolling, what is the linear speed of the disk when it reaches the bottom of the ramp

Explanation / Answer

Using the conservation of energy of the system:

?PE = ?KE ; the change in potential energy = the change in kinetic energy

taking the reference origin to be the top of the ramp:

mg(0) - mg(-h) = final KE ; since the initial KE = 0

here I have used h as the height of the ramp and this is given by Lsin(?) ; where ? is the angle with the horizontal and L is the length of the ramp.

mgh = translational KE + rotational KE

mgh = (1/2)mv

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