Linear Speed? Angular Speed? Centripetal Acceleration?

Sep 2013
10
0
a toy car moves around a circular track that
has a diameter of 1.2m. It makes one
complete revolution in 12secs. calculate the
linear speed, angular speed and centripetal
acceleration.

can u pls tell me how to answer that?
 

ChipB

PHF Helper
Jun 2010
2,361
289
Morristown, NJ USA
Think it through this way:

You can calculate the distance around the track from geometry: Circumference = pi times diameter. If it makes one complete revolution in T=12 seconds then its linear velocity is distance traveled divided by time = pi x D/T.

The angular velocity is expressed in radians per second. One revolution = 2 pi radians, so the angular speed is 2 pi radians/12 seconds. The formula that you should remember is w = 2 pi/T, where w = angular velocity in radians/second and T = period of revolution.

The centripetal acceleration is calculated using a = w^2 R, where w = angular velocity in radians/second (which you just calculated) and R = radius. You should memorize this formula.