A wheel of radius R rolls without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of the center of the wheel?
Practice Questions
1 question
Q1
A wheel of radius R rolls without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of the center of the wheel?
Rω
ω/R
ω
R/ω
The linear velocity v of the center of the wheel is related to the angular velocity by v = Rω.
Questions & Step-by-step Solutions
1 item
Q
Q: A wheel of radius R rolls without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of the center of the wheel?
Solution: The linear velocity v of the center of the wheel is related to the angular velocity by v = Rω.
Steps: 6
Step 1: Understand that the wheel is rolling without slipping, which means the point of contact with the ground is not sliding.
Step 2: Recognize that the angular velocity (ω) tells us how fast the wheel is spinning around its center.
Step 3: Know that the radius (R) is the distance from the center of the wheel to the edge.
Step 4: Realize that the linear velocity (v) of the center of the wheel is how fast the center is moving in a straight line.
Step 5: Use the relationship between linear velocity and angular velocity, which is given by the formula v = Rω.
Step 6: Conclude that to find the linear velocity of the center of the wheel, you multiply the radius (R) by the angular velocity (ω).
