# The Awesome Bowling Robot Is Surely Fake. Here's How to Tell

It really doesn't matter if it's real or fake (but it's surely fake—even Snopes says so). This spinning robot arm that bowls just looks awesome. Even better, it's a great chance to talk about some physics. In fact, I would recommend reading this Twitter thread with physics teachers talking about the video. It's great.

But like I said, it's fake. So, why is it fake? Here are some things we can look at.

### Motion of the Ball in the Air

The ball goes from the robot arm all the way to the bowling pins without hitting the ground. After the ball leaves the arm, there is only the gravitational force pulling downward (assume the air resistance force is negligible). That's exactly the same as projectile motion in your introductory physics course. The key to this kind of motion is that the horizontal and vertical motion of the ball can be treated independently. Since there isn't a horizontal force on the bowling ball (after it leaves the throwing arm) it would travel with a constant horizontal velocity. In the vertical direction, the ball starts with zero vertical velocity and then accelerates downward at 9.8 meters per second per second (due to the gravitational force).

But that makes analysis a little simpler. If the ball is launched horizontally (that's at least how it appears), I can get the launch speed by measuring the time it takes to travel to the bowling pins. Oh, it's fast—that's why I'm going to use my favorite (and free) video analysis tool: Tracker Video Analysis.

From the video, the ball takes 0.767 seconds to travel the length of a bowling lane, a distance of 18.29 meters (60 feet). This gives a horizontal velocity of:

This launch velocity of 23.85 m/s (53 mph) is the launch speed of the ball only for the case in which it is shot out with no vertical velocity component. If we consider the vertical direction, the ball will drop for the same amount of time that it takes to travel down the lane. Since I know that time and the vertical acceleration, I can calculate this vertical drop.

Note that this assumes the starting y-position is zero meters and the starting y-velocity is zero m/s (oh, and g = 9.8 m/s2). This gives a vertical drop of 2.88 meters (9.4 feet). So yeah—that ball couldn't be launched horizontally with that speed and make it all the way to the pins without hitting the ground. You would either have to launch it with a faster speed or launch it at a non-zero angle. I will leave both of those calculations to you for homework.

### Motion of the Spinning Arm

I already have an estimate for the launch speed of the ball from the time it takes to get down the lane. But how does this compare to the rotation rate of the robot arm? Let's just measure it. Again, using video analysis I can look at the time it takes to rotate. In this case I marked the time when the ball is at the bottom of the rotation cycle. Then I can plot the angular position (in radians) as a function of time. Here's what I get.

You can see that the rotation rate does indeed increase as time goes on and the robot arm gets up to throwing speed. By looking at the slope of this line near the end, I can get a final rotation rate. This puts the angular velocity at 93.65 radians per second.

OK, but there is a connection between the angular velocity and the launch velocity. If the ball is moving around in a circle with a radius r with an angular velocity ω, then the following must be true.

If the bowling ball has a diameter of 21 cm, then the circular radius of motion from the robot arm would be 40.5 cm (from video analysis). That would put the ball's launch velocity at 42 m/s (94 mph)—which is quite a bit faster than the measured velocity based on the time to move down the lane.

Working backward from the previous launch velocity, I can find another value for the rotation speed. If the ball is launched with a speed of 23.85 m/s, then the robot arm would have an angular velocity of 53 radians per second.

### Forces to Hold the Ball

So, I now have two rotation rates for the robot arm. One value is based on the measured launch speed and the other value is based on the measured angular position of the arm. But either way, if there is a ball moving in a circle, there needs to be a force acting on it. That force is from those robot gripper finger things (I guess those are robot fingers).

Any object that moves in a circle has an acceleration. This is because acceleration is defined as a the time rate of change of velocity—and velocity is a vector. So just changing the direction of motion is indeed an acceleration. The value of this acceleration depends on both the rotation rate and the radius of the circle. This acceleration has the following magnitude.

How do you get an object to accelerate? You apply a force. In this case there must be a force pushing the ball toward the center of the circle to get it to accelerate. That force would have to be the product of the acceleration and the mass.

# fma

I can calculate the acceleration (based on both estimates for angular velocity) and I can approximate the ball mass at 4.5 kilograms (for a 10-pound ball). That would put the required robot force at either 1,138 newtons or 3,552 newtons (256 or 799 pounds). Even at the lower estimated force, this is fairly high. Oh sure, a robot could hold on to a ball with superhuman forces—but in this case it is just using frictional forces.

How about another homework question? Suppose the coefficient of static friction between the ball and the "fingers" is 0.8. What compressive force would need to be applied to hold on to the ball?

### Even MORE Questions

If you want to play with this video some more, here are some other things for you to consider:

• What about the timing of the release? Pick one of the angular velocities along with the correct angle of release so that the ball hits the pins without first hitting the floor. What if the ball is released 0.01 seconds too late or too early? How much would this delay change the trajectory of the ball?
• Speaking of release: Notice that in the video, the ball appears to be released at the top of the circular motion at a point where the ball should be traveling away from the bowling pins. Yes, that's crazy.
• Estimate the kinetic energy of the ball and the time it takes to get the ball up to maximum rotation speed. What power (in watts) does this require?
• Use the approximate ball speed and mass. Estimate how much energy should go to the pins during impact. If these pins were then shot straight up (they aren't), how high would they go?
• Is it reasonable to ignore air resistance for this situation?
• Estimate the force required to hold the robot down to the floor during this shot.

### Fake Shake

One more thing. One way to make a fake video is to use a real video and then add special effects. It's probably much easier to add special effects to a video that was recorded with a camera on a tripod. However, it might not seem as genuine to use a tripod as it would to have someone just holding a camera. But handheld cameras shake a little bit. So a fake video could add some fake camera shake after the special effects were added.

I think that's what happened here. If you plot the motion of the background for the BowlBot video, you get this.

But what if you repeat something like this with a real hand-held camera? You should get something like this:

In my experience, real camera shakes are much more random-looking and not so smooth. Actually, a camera shake is very similar to a random walk. OK, there is the possibility that there is real camera shake on the bowling video and then someone used software to smooth it out. But still, that shake doesn't look normal.

Even if that BowlBot is fake—it probably won't be too long before someone builds a real one.

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