Question

Name a type of motion where an object does not change its speed but its direction of motion changes continuously. Calculate the speed of the tip of the second's hand of a watch of length 1.5 cm.

Answer 1

its uniform circular motion ,where an object does not changes its speed but it direction of motion changes continuously.
hope this would help you.

Answer 2

The type of motion which does not change but its direction of motion is circular motion or uniform motion. The speed of the second’s hand is $1.6\times10^{-3}\;m/s$

• Uniform motion is said to be the motion of a body along the circumference of the circle.
• When a body moves in a circular motion the speed at which it is moving remains constant while its direction of motion changes constantly as the displacement at each point on the circle keeps varying, represented by the tangents drawn at each point on the circle.
• The velocities at different points on the circle points to different directions and hence it is said that the direction of motion varies continuously.
• The velocity quantity as we know depends on both the magnitude as well as the direction of motion as it is a vector quantity.
• The direction of motion of the body also keeps changing in-order for it to cover a circular path. Thus, the velocity is what changes.
• However the speed which is known to be the magnitude of velocity only depends on the value and not direction parameter thus making it a scalar quantity.
• Hence, the speed with which the body is traveling (which is indicated by the magnitude) does not change and is constant.

In-order to calculate the speed of the hand of the clock we use the formula given below:

                                          $Speed=\frac{Distance}{Time} -------(1)$

• The second’s hand is the hand of the clock that moves continuously along with the minute and hour hand of the clock. For every second the hand of the clock moves some distance.
• The tip of the second’s hand moves along the circular path of the clock. We know that the seconds hand of the clock takes 1 minute to complete one full revolution which means that the distance covered by it is the entire arc which is equivalent to 2pir radian.
• In a single minute the second’s hand travels 360 degrees on the clock circle and this time period will be 1 minute or 60 seconds.

Thus, we have:

$Distance=2\pi r$

$Time=60\;s$

By substituting these values in the above equation (1) we get:

$Speed=\frac{2\pi r}{60}$

$\implies \frac{2\times3.14\times 1.5\times10^{-2} }{60}$

On solving the above equation we get:

$\implies Speed=1.571\times10^{-3}$

$\implies Speed=1.6\times10^{-3}\;m/s$

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