If a rolling object has a translational speed of v and a rotational speed of ω, what is the relationship between them for rolling without slipping?
Practice Questions
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Q1
If a rolling object has a translational speed of v and a rotational speed of ω, what is the relationship between them for rolling without slipping?
v = ωR
v = 2ωR
v = ω/R
v = R/ω
For rolling without slipping, the relationship is v = ωR, where v is the translational speed and ω is the angular speed.
Questions & Step-by-step Solutions
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Q
Q: If a rolling object has a translational speed of v and a rotational speed of ω, what is the relationship between them for rolling without slipping?
Solution: For rolling without slipping, the relationship is v = ωR, where v is the translational speed and ω is the angular speed.
Steps: 5
Step 1: Understand that 'rolling without slipping' means the object rolls on a surface without sliding.
Step 2: Identify the terms: 'v' is the translational speed (how fast the center of the object moves), and 'ω' is the rotational speed (how fast the object spins around its axis).
Step 3: Recognize that when an object rolls without slipping, the point of contact with the ground is momentarily at rest.
Step 4: Relate the translational speed 'v' to the rotational speed 'ω' using the radius 'R' of the object.
Step 5: The formula that connects these speeds is v = ωR, meaning the translational speed equals the rotational speed multiplied by the radius.
