A ball rolls without slipping on a flat surface. What is the relationship between its linear velocity and angular velocity?
Practice Questions
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Q1
A ball rolls without slipping on a flat surface. What is the relationship between its linear velocity and angular velocity?
v = ωR
v = 2ωR
v = ω/2R
v = R/ω
For rolling without slipping, the relationship is v = ωR, where v is linear velocity, ω is angular velocity, and R is the radius.
Questions & Step-by-step Solutions
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Q
Q: A ball rolls without slipping on a flat surface. What is the relationship between its linear velocity and angular velocity?
Solution: For rolling without slipping, the relationship is v = ωR, where v is linear velocity, ω is angular velocity, and R is the radius.
Steps: 5
Step 1: Understand that the ball is rolling without slipping, which means it is not sliding on the surface.
Step 2: Identify the terms: 'v' is the linear velocity (how fast the ball moves in a straight line), 'ω' is the angular velocity (how fast the ball is spinning), and 'R' is the radius of the ball (the distance from the center to the edge).
Step 3: Realize that when the ball rolls, the point of contact with the surface is momentarily at rest, meaning the distance it rolls forward is equal to the distance it spins.
Step 4: Use the formula v = ωR to express the relationship: the linear velocity (v) is equal to the angular velocity (ω) multiplied by the radius (R).
Step 5: Conclude that if you know any two of these values (v, ω, R), you can find the third using this relationship.
