Question

information about two gears is shown in the table.

which statements compare the angular and linear velocities of the gears? check all that apply.
gear 1 has a greater angular velocity than gear 2.
gear 1 has a lesser angular velocity than gear 2.
gear 1 has a greater linear velocity than gear 2.
gear 1 has a lesser linear velocity than gear 2.

Explanation:

Step1: Calculate angular velocity

Angular velocity formula: \(\omega = 2\pi n\) (where \(n\) is revolutions per minute).
For Gear 1: \(\omega_1=2\pi\times60 = 120\pi\) rad/min.
For Gear 2: \(\omega_2=2\pi\times80=160\pi\) rad/min.
Since \(120\pi<160\pi\), Gear 1 has a lesser angular velocity than Gear 2.

Step2: Calculate linear velocity

Linear velocity formula: \(v=\omega r\).
For Gear 1: \(v_1 = 120\pi\times6=720\pi\) in/min.
For Gear 2: \(v_2=160\pi\times4 = 640\pi\) in/min.
Since \(720\pi>640\pi\), Gear 1 has a greater linear velocity than Gear 2.

Answer:

B. Gear 1 has a lesser angular velocity than Gear 2.
C. Gear 1 has a greater linear velocity than Gear 2.