Gear A, with a mass of 1.00 kg and a radius of 55.0 cm is in contact with gear B, with a mass

step 1 The two gear A and B are in contact. Let's say these are the two gear. This one is gear A and th

Gear A, with a mass of 1.00 kg and a radius of 55.0 cm is...

Gear $A$, with a mass of $1.00 \mathrm{~kg}$ and a radius of $55.0 \mathrm{~cm}$ is in contact with gear $\mathrm{B}$, with a mass of $0.500 \mathrm{~kg}$ and a radius of $30.0 \mathrm{~cm} .$ The gears do not slip with respect to each other as they rotate. Gear A rotates at 120. rpm and slows to 60.0 rpm in $3.00 \mathrm{~s}$. How many rotations does gear B undergo during this time interval?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Gear Ratios and the Non?Slip Condition

When two gears are in contact without slipping, the tangential speeds at the point of contact are equal. This provides a relationship between the angular velocities of the gears, which is determined by their radii (or number of teeth). The gear ratio then becomes a crucial concept as it allows us to relate the rotation of one gear to the rotation of the other. The number of rotations of one gear can be deduced from that of the other by a factor equal to the ratio of their radii, ensuring the preservation of the non?slipping condition.

Rotational Kinematics

Rotational kinematics deals with the motion of objects as they rotate. It includes concepts such as angular displacement, angular velocity, and angular acceleration. In problems of this nature, one would apply equations analogous to the linear motion equations, such as calculating the angular displacement during a period of uniformly changing angular speed. This also involves converting between units, such as revolutions per minute (rpm) to radians per second, and then using those values to determine the magnitude of rotation over time.

Transcript

Please give Ace some feedback