a disk with a radius of 1.20 cm rolls in a straight line across a flat, horizontal surface. if the disk has an initial angular speed of 18.0 rad/s and slows at a rate of 1.90 rad/s2, how far does it roll before coming to rest? (assume there is no slipping and it does not tip over).

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21-11-2022
Physics

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a disk with a radius of 1.20 cm rolls in a straight line across a flat, horizontal surface. if the disk has an initial angular speed of 18.0 rad/s and slows at a rate of 1.90 rad/s2, how far does it roll before coming to rest? (assume there is no slipping and it does not tip over).

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hritviks993 hritviks993 · Answer 1 · 2022-11-24T23:42:22-05:00

A disk with a radius of 1.20 cm rolls in a straight line across a flat, horizontal surface. If the disk has an initial angular speed of 18.0 rad/s and slows at a rate of 1.90 rad/s2 and the disc comes to rest after covering 1.023 m.

What is angular velocity?

Angular velocity can be defined as the time rate at which an object will rotates and if it revolves, about an axis in which the angular displacement between two bodies changes.

To find the displacement,

Initial angular speed, wo = 18 rad/s

final angular speed, w = 0 rad/s

angular acceleration, = 1.9 rad/s²

radius, r = 1.2 cm = 0.012 m

initial linear velocity, u = r wo

= 0.012 x 18 = 0.216 m/s

final linear speed, v = r w

= 0.012 x 0 = 0 m/s

linear acceleration, a = r x angular acceleration

= 0.012 x 1.9 = 0.0228 m/s2

Let the distance traveled is s.

Using third equation of motion

V² = U²+2as

0 =0.216²+2×0.0228×s

s = 1.023m

The disc comes to rest after covering 1.023 m.

Learn more about Angular velocity,

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