Question

Tom and Mary are riding a merry-go-round. Tom is on a horse about half way between the center and the outer rim, and Mary is on a horse at the outer rim.
a) Which child has the larger angular speed? Explain



b) Which child has the larger linear speed? Explain



c) Which child has the larger radial acceleration? Explain

Answer 1

Answer:

Explanation:

Given

Tom is on half way between the center and the outer rim

Mary is on the extreme outer rim

Suppose $\omega$ is the angular velocity of ride with radius of outer rim be R

$\alpha =$angular acceleration of Ride

At any instant both Tom and Mary experience the same angular speed

(b)Linear velocity at any instant

$v_{Tom}=\omega \times R$

$v_{Mary}=\omeag \times \frac{R}{2}$

Thus Tom has higher linear speed

(c) For radial Acceleration

$a_r=\omega ^2\times r$

$a_{Tom}=\omega ^2\times R$

$a_{Mary}=\omega ^2\times \frac{R}{2}$

Tom has higher radial Acceleration as it is directly Proportional of radius