If the radius of a rotating wheel is halved while keeping the angular velocity constant, what happens to the linear velocity of a point on the edge of the wheel?
Practice Questions
1 question
Q1
If the radius of a rotating wheel is halved while keeping the angular velocity constant, what happens to the linear velocity of a point on the edge of the wheel?
It doubles
It halves
It remains the same
It becomes zero
Linear velocity v = rω; if r is halved and ω remains constant, v is halved.
Questions & Step-by-step Solutions
1 item
Q
Q: If the radius of a rotating wheel is halved while keeping the angular velocity constant, what happens to the linear velocity of a point on the edge of the wheel?
Solution: Linear velocity v = rω; if r is halved and ω remains constant, v is halved.
Steps: 6
Step 1: Understand that the linear velocity (v) of a point on the edge of a wheel is calculated using the formula v = rω, where r is the radius and ω is the angular velocity.
Step 2: Note that in this scenario, the radius (r) of the wheel is being halved. This means if the original radius was r, the new radius will be r/2.
Step 3: Recognize that the angular velocity (ω) remains constant, meaning it does not change.
Step 4: Substitute the new radius into the formula: v = (r/2)ω.
Step 5: Compare the new linear velocity with the original: the original linear velocity was v = rω, and the new linear velocity is v = (r/2)ω.
Step 6: Since (r/2)ω is half of rω, the new linear velocity is half of the original linear velocity.
