A disk rotates about its axis with an angular velocity of ω. If its radius is do
Practice Questions
Q1
A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular velocity to maintain the same linear velocity at the edge?
ω/2
ω
2ω
4ω
Questions & Step-by-Step Solutions
A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular velocity to maintain the same linear velocity at the edge?
Correct Answer: ω
Step 1: Understand that the linear velocity (v) at the edge of the disk is given by the formula v = rω, where r is the radius and ω is the angular velocity.
Step 2: Identify that if the radius (r) is doubled, the new radius becomes 2r.
Step 3: Write the formula for the new linear velocity with the new radius: v' = (2r)ω'.
Step 4: To maintain the same linear velocity (v = v'), set the two equations equal: rω = (2r)ω'.
Step 5: Simplify the equation by dividing both sides by r (assuming r is not zero): ω = 2ω'.
Step 6: Solve for the new angular velocity (ω'): ω' = ω/2.
Step 7: Conclude that to maintain the same linear velocity at the edge when the radius is doubled, the new angular velocity must be half of the original angular velocity.
Angular Velocity and Linear Velocity Relationship – The relationship between linear velocity (v), angular velocity (ω), and radius (r) is given by the equation v = rω. This concept tests the understanding of how changes in radius affect angular velocity when linear velocity is to be maintained.
