Centripetal Acceleration Concepts

The video tutorial explains how centripetal acceleration is affected by changes in linear speed and radius. It begins with a van driving around two curves of the same radius but different speeds, demonstrating how the centripetal acceleration decreases by a factor of nine when the speed is reduced to one-third. The tutorial then presents another example involving angular speed, where a father spins his daughter in circles of different radii, showing that the centripetal acceleration increases by a factor of two when the radius is doubled.

What is the relationship between linear speed and centripetal acceleration?

• Centripetal acceleration is directly proportional to linear speed.

• Centripetal acceleration is inversely proportional to the square of linear speed.

• Centripetal acceleration is inversely proportional to linear speed.

• Centripetal acceleration is directly proportional to the square of linear speed.

For the first curve, if the linear speed is v, what is the formula for centripetal acceleration?

• v/r

• v^2/r

• r/v

• r^2/v

How does the centripetal acceleration change when the van's speed is reduced to one-third on the second curve?

• It increases by a factor of 9.

• It decreases by a factor of 9.

• It decreases by a factor of 3.

• It remains the same.

What is the factor by which the centripetal acceleration decreases when the van's speed is reduced to one-third?

• Factor of 12

• Factor of 9

• Factor of 6

• Factor of 3

In the example of the father spinning his daughter, what happens to the centripetal acceleration when the radius is doubled?

• It remains the same.

• It decreases by a factor of 2.

• It increases by a factor of 4.

• It increases by a factor of 2.

What is the formula for centripetal acceleration in terms of angular speed?

• omega^2 / r

• omega / r

• r * omega

• r * omega^2

If the angular speed remains constant and the radius is doubled, how does the centripetal acceleration change?

• It increases by a factor of 4.

• It decreases by a factor of 2.

• It remains the same.

• It increases by a factor of 2.

What is the initial centripetal acceleration when the radius is r and angular speed is omega?

• omega^2 / r

• r * omega

• r * omega^2

• omega / r

How does the centripetal acceleration change when the radius is increased to 2r while maintaining the same angular speed?

• It increases by a factor of 4.

• It decreases by a factor of 2.

• It remains the same.

• It increases by a factor of 2.

What is the final centripetal acceleration when the radius is 2r and angular speed is omega?

• 2r * omega

• 2r * omega^2

• omega^2 / 2r

• omega / 2r