If a disc rolls without slipping on a flat surface, what is the relationship bet

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Question: If a disc rolls without slipping on a flat surface, what is the relationship between its linear velocity v and angular velocity ω?

Options:

Correct Answer: v = rω

Solution:

For rolling without slipping, the linear velocity v is equal to the radius r times the angular velocity ω, hence v = rω.

If a disc rolls without slipping on a flat surface, what is the relationship between its linear velocity v and angular velocity ω?

If a disc rolls without slipping on a flat surface, what is the relationship between its linear velocity v and angular velocity ω?

Step 1: Understand that a disc rolling without slipping means that the point of contact between the disc and the surface does not slide.
Step 2: Recognize that the disc has a radius 'r'.
Step 3: Know that the disc rotates around its center as it rolls.
Step 4: The angular velocity 'ω' tells us how fast the disc is spinning around its center.
Step 5: The linear velocity 'v' tells us how fast the disc is moving forward on the surface.
Step 6: When the disc rolls without slipping, the distance it travels forward (linear distance) is equal to the distance it rotates (circumference of the circle).
Step 7: The relationship between linear velocity 'v' and angular velocity 'ω' is given by the formula: v = r * ω.

Rolling Motion – The relationship between linear and angular velocity for objects rolling without slipping.
Kinematics – Understanding the connection between linear and angular quantities in motion.