Auniform solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane. if the angular velocity of the disk is 5.35 rad/s at the bottom, what is the height of the inclined plane?

To solve this problem we will use the concepts related to energy conservation. Both potential energy, such as rotational and linear kinetic energy, must be conserved, and the gain in kinetic energy must be proportional to the loss in potential energy and vice versa. This is mathematically

Where,

m = mass

v = Tangential Velocity

= Angular velocity

I = Moment of Inertia

g = Gravity

Replacing the value of Inertia in a Disk and rearranging to find h, we have

Replacing,

Therefore the height of the inclined plane is 5.6m

0.19 m/s and 0.45 m/s

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)