Jessica is riding on a merry-go-round on an outer horse that sits at a distance
of 8.0 m from the center of the ride. Jessica\'s sister, Julie, is on an inner horse
located 6.0 m from the ride\'s center. The merry-go-round turns around once
every 40.0 s. a) Explain which girl is moving with the greater linear speed.
b) What is the centripetal acceleration of Julie and her horse?
0 (0 stars)
0
180 response - 0 helps

a. Jessica's has a greater linear speed.

b. The centripetal acceleration of Julie and her horse is 0.148 m/s².

### a) Explain which girl is moving with the greater linear speed.

Jessica's has a greater linear speed.

To answer the question, we need to know what Linear speed is.

### What is linear speed?

This is the tangential speed at which an object in circular motion moves. It is given by v = rω where

• r = distance of object from center of circle and
• ω = angular speed.

Now, given that Jessica is riding on a merry-go-round on an outer horse that sits at a distance of 8.0 m from the center of the ride and Jessica's sister, Julie, is on an inner horse located 6.0 m from the ride's center. Also, the merry-go-round is moving at constant angular speed.

Since Linear speed v = rω and ω = constant,

So, v ∝ r.

So, the girl with the greater distance from the center of the merry-go-round would have the greater linear speed.

Since

• Jessica is at r' = 8.0 m and
• Julie is at r" = 6.0 m.

Since

• v ∝ r, and
• r' = 8.0 m > r" = 6.0 m,

So, Jessica's has a greater linear speed.

### b) What is the centripetal acceleration of Julie and her horse?

The centripetal acceleration of Julie and her horse is 0.148 m/s².

Centripetal acceleration a = rω² where

• r = distance of Julie from center of merry-go-round = 6.0 m and
• ω = angular speed of merry go round.

Since the merry-go-round turns once every 40.0 s, we have that ω = 2π/40.0 s

= π/20.0 s

Since a = rω²

Substituting the values of the variables into the equation, we have

a = rω²

a = 6.0 m × (0.157 rad/s)²

a = 6.0 m × 0.0247 rad²/s²

a = 0.148 m/s²

So, the centripetal acceleration of Julie and her horse is 0.148 m/s².