A wheel of radius R rolls without slipping on a horizontal surface. If the wheel
Practice Questions
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
Questions & Step-by-Step Solutions
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?
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).
Relationship between Angular and Linear Velocity – The linear velocity of a point on a rotating object is directly proportional to its angular velocity and the radius of the rotation.
