Peoples Physics Book Version-2

http://www.ck12.org Chapter 10. Rotational Motion Version 2

10.4 Example 1

Question: A game of tug-of-war is played... but with a twist (ha!). Each team has its own rope attached to a merry-
go-round. One team pulls counterclockwise with a force of 200N. The other team pulls clockwise with a force of
400N. But there is another twist. The counterclockwise team’s rope is attached 2.6m from the center of the merry
go round and the clockwise team’s rope is attached 1.2m from the center of the circle.

a) Who wins?

b) By how much? That is, what is the net torque?

c) Assume that the merry-go-round is weighted down with a large pile of steel plates. It is so massive that it has a
moment of inertia of 2000kg×m^2. What is the angular acceleration?

d) How long will it take the merry-go-round to complete one revolution?

Solution:

a) To find out who wins, we need to find which team is pulling with the greater torque. Therefore, we will use the
equation

τ=rF

counterclockwise team:

τ=rF= 2 .6m×200N=520N×m

clockwise team:

τ=rF= 1 .2m×400N=480N×m

So the counterclockwise team wins.

b) To figure out the net torque we simply subtract the two torques.

520N×m−480N×m=40N×m

So we have a 40N×m counterclockwise net torque.

c) To find the angular acceleration we use the equation

α=

τ

l

Since we know both the net torque and the moment of inertia, all we have to do is plug these values in.

α=

τ

l

=

40N

2000kg×m^2

=.02r/s^2

d) Finally, we want to know the time of one rotation. To do this we will use the equation

θ=θi+wit+

1

2

αt^2