Question

The hour hand on a certain clock is 8.2 cm long. Find the tangential speed of the tipof this hand.
1 µm/s

Answer 1

Concepts and reason

The concept used to solve this problem is tangential speed.

Initially, use relation between angular velocity and position to find the angular velocity.

Then, use relation between tangential speed and angular velocity to find the tangential speed of the tip of the hour hand.

Fundamentals

Tangential speed is the linear speed of an object moving along a circular path.

$v=ro $

Here, is the tangential speed, is the radial distance and is the angular velocity.

The expression for angular velocity is given by,

Here, is the change in position and is the time.

The total distance travelled by the hour hand is equal to the circumference of the circle. Then, the change in position in the motion is,

The expression for angular velocity is,

Substitute for and for .

Tangential speed of the tip of the hour hand is,

$v=ro $

Substitute for and for .

Ans:

Thus, the tangential speed of the tip of the hour hand is .