Question

Can someone help me answer this linear momentum problem, thanks?

The linear momentum of a 40.0kg object moving around a 90.0m circle at a constant speed of 7.60m/s is ____Answer should be in Newtons

Answer 1

The momentum is `304 N*s`.

Explanation:

The linear momentum, `p`, of a 40.0kg object moving at a constant speed of 7.60m/s is
`p = m*v = 40.0 kg*7.60 m/s = 304 (kg*m)/s`

Your question says that the answer should have units on Newtons. That is incorrect. I am certain that the intention was to say "the answer should have units of `"Newton"*s`". The combination of units `(kg*m)/s` is also valid for momentum, so that could have been used with the answer to this question -- except for the instruction to use `N*s`.

Justification:
Consider Newton's 2nd Law -- often abbreviated as F=ma. It means that if `1 kg " is accelerated at " 1 m/s^2, "the net force causing that is " 1 N`
The formula with that data in it would be `1 N = 1 kg*1m/s^2`.
Therefore the Newton is equivalent to `(kg*m)/s^2`.

Therefore, when you use `N*s`, the s in the numerator cancels the `" "^2` in the denominator.

So your answer should be `304 N*s` or `304 "Newton"*s`.

I hope this helps,
Steve