A coin with a radius of 5 cm rolls down a 30° inclined plane in a straight line without slipping. When the coin is at a height of 50 cm above the ground, it's angular speed is 45.0 rad/s. If the moment of inertia of the coin is (1/2) MR2, what will be the velocity of the coin when it reaches the ground ?

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Chapter1: Units, Trigonometry. And Vectors
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A coin with a radius of 5 cm rolls down a 30° inclined plane in a straight line
without slipping. When the coin is at a height of 50 cm above the ground,
it's angular speed is 45.0 rad/s. If the moment of inertia of the coin is
(1/2) MR2, what will be the velocity of the coin when it reaches the ground ?
Transcribed Image Text:A coin with a radius of 5 cm rolls down a 30° inclined plane in a straight line without slipping. When the coin is at a height of 50 cm above the ground, it's angular speed is 45.0 rad/s. If the moment of inertia of the coin is (1/2) MR2, what will be the velocity of the coin when it reaches the ground ?
Expert Solution
Step 1

Assume that the ground will be the datum point.

On the system, no external force is acting on this. Therefore, from conservation of energy.

Physics homework question answer, step 1, image 1

The formula for the angular velocity in terms of linear velocity is:

Physics homework question answer, step 1, image 2

Step 2

Use the expression of the angular velocity, and known values and rewrite the expression of energy as:

Physics homework question answer, step 2, image 1

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