Question

A cyclist pedals to exert a torque on the rear wheel of the bicycle. When the cyclist changes to a higher gear, the torque increases. Which of the following would be the most effective strategy to help you determine the change in angular momentum of the bicycle wheel?a. multiplying the ratio between the two torques by the mass of the bicycle and riderb. adding the two torques together, and multiplying by the time for which both torques are appliedc. multiplying the difference in the two torques by the time for which the new torque is appliedd. multiplying both torques by the mass of the bicycle and rider

Answer 1

c. multiplying the difference in the two torques by the time for which the new torque is applied

Step-by-step explanation:

For a particle moving in a circular orbit, the angular momentum is

L = r x p = m r2 ω.

For a continuous mass distribution, L = ∫ dm r2 ω = Iω

Angular momentum is a vector that is parallel to the angular velocity.

If there is no net torque acting on a system, the system's angular momentum is conserved.

A net torque produces a change in angular momentum that is equal to the torque multiplied by the time interval over which the torque is applied. From Newton's second law for rotational motion,

ΔL = Δt*τ

In differential form,

Στ = dLdt = d(Iω)dt = Idωdt+ ω

Integrating the general equation gives: ∫ ∑ τ dt = ΔL

The net torque equals the rate of change of the angular momentum.

The net torque acting over a time interval is the angular impulse.

Answer 2

Option C

multiplying the difference in the two torques by the time for which the new torque is applied.

Step-by-step explanation:

Torques is a rotational force and it is the rate change of angular momentum expressed by:

T= ∆L/∆t eqn.1

where T= torque

∆L = Angular momentum

∆t= time difference

Angular momentum can now be expressed as ∆L= T × ∆t. eqn.2

From the eqn. 2 it can be deducted that angular momentum can be expressed by multiplying the difference in the two torques by the time for which the new torque is applied.