A wheel of radius R rolls without slipping on a horizontal surface. If it rotate
Practice Questions
Q1
A wheel of radius R rolls without slipping on a horizontal surface. If it rotates with an angular velocity ω, what is the linear velocity of the center of the wheel?
Rω
2Rω
ω/R
R/ω
Questions & Step-by-Step Solutions
A wheel of radius R rolls without slipping on a horizontal surface. If it rotates with 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: Recall that the angular velocity (ω) tells us how fast the wheel is spinning around its center.
Step 3: Recognize that the radius (R) of the wheel 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: Substitute the values of R and ω into the formula to find the linear velocity v.
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.
