Question

A Formula One race car with mass 750.0 kg is speeding through a course in Monaco and enters a circular turn at 220.0 km/h in the counterclockwise direction about the origin of the circle. At another part of the course, the car enters a second circular turn at 180 km/h also in the counterclockwise direction. If the radius of curvature of the first turn is 130.0 m and that of the second is 100.0 m, compare the angular momenta of the race car in each turn taken about the origin of the circular turn.

a) Angular momentum in the first turn is greater.
b) Angular momentum in the second turn is greater.
c) Angular momenta are equal in both turns.
d) Cannot be determined from the given information.

Answer 1

The angular momentum of an object depends on its angular velocity and moment of inertia. In this case, the race car will have a larger angular momentum in the first turn due to its higher linear velocity and larger radius of curvature.

Step-by-step explanation:

The angular momentum of an object is given by the formula:

L = Iω

Where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

In this case, the moment of inertia does not change as the car moves through the circular turns, so the comparison of angular momenta depends solely on the angular velocity.

The angular velocity of an object moving in a circular path is given by the formula:

ω = v/r

Where v is the linear velocity and r is the radius of curvature.

Comparing the angular velocities of the car in each turn, we find that the angular momentum will be greater in the turn with the higher linear velocity and larger radius of curvature.

Therefore, the answer is Angular momentum in the first turn is greater.

Answer 2

By applying the formula for angular momentum, which is L = mvr, we find that the angular momentum in the first turn is greater than in the second turn. Option a is correct.

Step-by-step explanation:

To compare the angular momenta of a Formula One race car in each circular turn, we can use the formula for angular momentum L = mvr, where m is mass, v is tangential speed, and r is the radius of curvature. The car's mass m is 750.0 kg for both turns.

For the first turn:

• Convert the speed from km/h to m/s: v = 220 km/h = 220 * 1000/3600 m/s = 61.11 m/s.
• Angular momentum L1 = m * v1 * r1 = 750 kg * 61.11 m/s * 130 m = 5,942,250 kg*m2/s.

For the second turn:

• Convert the speed from km/h to m/s: v = 180 km/h = 180 * 1000/3600 m/s = 50.00 m/s.
• Angular momentum L2 = m * v2 * r2 = 750 kg * 50.00 m/s * 100 m = 3,750,000 kg*m2/s.

Comparing L1 and L2, we see that L1 is greater than L2. Therefore, the angular momentum in the first turn is greater.