CRJ 200 Captain reported they felt a sharp left yaw torque during takeoff. The reporter could not determine the cause and after performing a flyby at their destination it was determined there were no anomalies and the flight landed safely.

Narrative

On take-off from Runway XXR at ZZZ; right after V1; but before rotating; we both felt a sharp left yaw torque on the plane. Vr took about 3 or 4 seconds longer to get to than we are used to. There was some gusty wind; but not THAT bad. We were still right near centerline; as it was sharp but of short duration. We both agreed about the feeling and the slow acceleration after take-off. We had no other anomalies; no noises; and no Engine Indicating and Crew Alerting System messages. Both of us pilots discussed this during the climb-out. I asked the flight attendant if she'd heard any noise or felt this jerk. She had not heard noise; but had felt the motion. We both speculated if this was a tire problem; so I wrote Maintenance Control; with cc to dispatcher with solicitation of ideas. Maintenance eventually asked about anti-skid or brake overheat; but we replied in the negative. We considered that the anti-skid caution message doesn't last long until the gear comes up; so we could have missed it. We also considered whether one of us had been on one brake during Take-off; but that was not likely. After one more query of Maintenance; with no reply recommendation; I noted that with the strong crosswinds and medium to short runway at ZZZ1; we'd be erring on the side of caution by checking this out before just setting down. Considering the fact that we could have to leave the gear down (for a tire problem) or need 1.75 times the runway (for an anti-skid problem - not requiring a fly-by; of course); we saw that with our decent amount of extra fuel (1100 lbs.) we could get to ZZZ2 safely no matter what. (Still crosswinds; but 9000 ft.) I wrote dispatcher to let her know the plan. While I did that; I asked the non-flying pilot to let the Flight Attendant first; and then the passengers; know that'd we'd do a low fly-by just to check out a possible tire problem. The Flight Attendant at one point said one pilot on board wanted to talk to me; so I talked for a minute on the intercom with him. A former R/J pilot; he understood what I'd said; but told me that he thought the P/A to the passengers wasn't clear. After we flew over at 400 ft. we were told no anomalies by both the Tower and 2 RJ pilots in the hold pad. As I did a VFR pattern back around; the non-flying pilot let the passengers know we were fine and we'd be down in 5 minutes. Due to major problems with gate space and personnel we had a 20 minute wait in a holding spot; during which I followed up with Maintenance and Dispatcher and then told the passengers more of the story. I noted no anomalies during post-flight walk-around inspection. We don't know any cause for the take-off anomaly. I'd just never felt this kind of jerk before; and figured we'd be safer checking it out.About the pilot-passenger and the announcement. I considered his opinion on the communication. However; I'd already discussed with the other pilot that we'd keep it short and just let them know we'd do this as a precaution; with no need for a bunch of details. I noted that the other pilot made it pretty quick; and she told me later it was pretty much like I'd said; just short with an explanation ahead of time of why we'd come in first without landing and with no reason to alarm anyone. I have trust in the other pilots to make good communications to the passenger. There was no reason for any preparations for the Flight Attendant; as there was no emergency. If we'd have found a problem; then we would have communicated with everyone; Maintenance; Dispatch; the Flight Attendant; and finally the passengers; about the new plan. This passenger-pilot apparently had a problem with our handling of this as he had complained to the Flight Attendant while the other pilot was looking for food and setting up things for the return (very late at this point); and I was post-flighting; checking/calculating the loads for the outbound flight; using the bathroom; and getting a candy bar. Neither of us had a chance to explain anything to him. Finally; I will say that ZZZ Approach and the ZZZ1 Tower were most helpful. Nothing needed to be expedited; but they communicated well and arranged things for us.