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It was going to be a tight Presidential Election in 1840. William Henry Harrison was running against incumbent, Martin Van Buren. Harrison used innovative techniques that foreshadowed modern campaign tactics.

His supporters went visual and big. They made a huge ball, about ten feet tall, loaded it up with campaign slogans, and physically rolled it from town-to-town. This is the origin of the phrase ‘Keep the Ball Rolling’. Some of the slogans on this ball were ‘Fare well Dear Van, not the man’, referring to opponent Martin Van Buren. Or ‘To Guide the ship, Old Tip’, referring to Harrison and his famous victory at Tippecanoe.

They had a song with a memorable tagline ‘Tippecanoe and Tyler Too’ The song itself is forgotten, but not the famous slogan.

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His opponent’s campaign fought back. They tried to exploit his age. At 67, he was the oldest candidate to-date. His opponents said Harrison was an old man who would be content to sit in his log cabin and drink hard cider. This backfired. Harrison’s campaigned embraced these descriptions. The campaign used the log cabin image to support Harrison as a common humble man versus the aristocratic Van Buren. Somewhat fake news, as Harrison was born into a well-off family in Virginia while Van Buren came from a poor family in upstate New York .

To get people to campaign rallies, the campaign provided hard cider. Hard cider was a common drink in those days and reinforced Harrison’s image as a common man. Imagine today a beer drinker running against a single malt scotch drinker.

Partisanship 1840 was rough. One example was the ‘Gold Spoon’ speech opposing Van Buren. This speech contrasted Harrison as a modest Frontier Man with Van Buren’s alleged luxurious life style. In one part it criticizes Van Buren for wanting a nice garden – “

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He [has] … constructed a number of clever sized hills, every pair of which, it is said, was designed to resemble and assume the form of an Amazon's bosom, with a miniature knoll or hillock on its apex, to denote the nipple.

I guess there was no “#MeToo” movement back in 1840. The speech was printed and distributed as campaign literature in support of Harrison.

Harrison won easily. The aggressive campaign run on his behalf resulted in one of the highest voter turnouts on record, over 80%. Both Harrison and Van Buren were the first candidates to receive over one million votes.

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Prior to the Presidency, Harrison had spent over forty years in public service. The Harrison family line is distinguished in our history. His father was one of the signers of the Declaration of Independence. His grandson, Benjamin Harrison, became the 23rd President of the Country, the only grandfather-grandson combination in our history to-date. He joined the military and was assigned to the ‘West’, which was near Cincinnati at the time. He later served as representative of the Northwest Territories to Congress and Governor of the Indiana Territory before rejoining the army for the war of 1812. Under his leadership, the Americans recaptured Detroit in 1813 and defeated a combined British-Indian force in Ontario, one of the largest American victories in that war.

There is controversy over the 1811 Tippecanoe battle, fought in Indiana. Originally intended as a show of force, Harrison’s forces significantly outnumbered the Indians consisting of the Shawnee and other tribes. His forces camped by the Tippecanoe River and were surprised by an Indian attack. He was later criticized for not fortifying his camp. While the Americans took more casualties than the Indians, his forces won the battle.

Harrison died after thirty days in office, the shortest Presidential term on record. The story that he died from exposure due to his long Inaugural speech in cold weather without adequate clothing turns out not to be accurate. He did not get sick until three weeks after his Inauguration and took nine days to die. Medical treatment of the day, including opium, probably did not help.

Solved A Ball Rolls Along A Track As Shown On The Left. (it

Harrison’s campaign was one of the first modern image based, grassroots campaigns. Before Harrison, candidates did not give speeches on their behalf. Harrison did. His campaign slogan, ‘Tippecanoe and Tyler Too’ is still recognized to this day. They used imagery, music and drink to develop support and turn out the vote. This is his main legacy to the country.Stack Exchange is a question and answer site for active researchers, academics and students of . It only takes a minute to sign up.

I was wondering about this question since I learned about rolling motion in the chapter on rotational mechanics. I was unable to come to a solid conclusion due to the reasons mentioned below.

The forces acting on the ball are shown in red and are the normal contact force $N$ and the gravitational force of attraction $mg$. I qualitatively determined the torque of these forces about two axes - one passing through the centre of mass of the ball of uniform density, and the other passing through the point of contact of the ball and the inclined plane. Both of these axes are perpendicular to the screen.

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When the axis passes through the centre of the ball, the torque exerted by $mg$ is zero as its line of action meets the axis. Further, the torque exerted by $N$ is also zero due to the same reason. There are no other forces. So, net torque about this axis is zero, and this tempts us to conclude the ball slides down the inclined plane.

When the axis passes through the point of contact, the torque exerted by $N$ is zero but the torque exerted by $mg$ is non-zero. This means the ball must roll i.e., it rotates while moving down the inclined plane. This conclusion is contradictory to the former case.

The following diagram is a visual interpretation of my question (if the terms slide and roll confuses the reader) where the red arrow denotes the orientation of the ball:

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Please Note: The question - Ball Rolling Down An Inclined Plane - Where does the torque come from? discusses the case of ball rolling on an inclined plane where friction is present. Since the question - Rolling in smooth inclined plane is marked as duplicate of the former, and has no sufficient details, I planned to ask a new question with additional information.

Actually, it means that the angular momentum about that axis must increase. That is not the same as rolling. If the axis is through the center of mass of the object then the only way for the angular momentum to increase is through rolling. However, if the axis does not pass through the center of mass then there is also angular momentum due to the linear motion. In other situations this is the difference between orbital angular momentum and spin angular momentum. So let's calculate the orbital angular momentum in this problem.

The torque is $m g R sin(theta)$ where $R$ is the radius of the ball and $theta$ is the angle of the incline.

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The magnitude of the orbital angular momentum is given by $R m v$ where $v$ is the linear velocity of the center of mass, so its time derivative is $R m a$ where $a$ is the linear acceleration of the center of mass.

From Newton's laws the linear acceleration is the component of gravity which is down the slope. This is $ma=mg sin(theta)$ so $a=g sin(theta)$.

Substituting the linear acceleration into the time derivative of the orbital angular momentum gives $R m g sin(theta)$ which is equal to the torque. This means that the increase in angular momentum due to the torque is fully accounted for by the increase in the orbital angular momentum and there is no left over torque for increasing the spin angular momentum. Therefore, the ball does not spin/roll regardless of which axis you examine.

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Frictionless means the surface of the incline cannot exert any torque on the ball. By Newton's second law, that means the state of rotation of the ball remains unaltered, specifically:

The ball will slide. You mistake was to choose an 'accelerating axis' (The point of contact through which the axis passes is accelerating). Note that the you can only form torque equation about the axis which are stationary or translating with constant velocity.

The beauty of centre of mass is that torque equation can be applied to an axis passing through C.O.M irrespective of whether that axis is accelerating or not. (That's why C.O.M is the most popular choice for applying torque equation). This property is only true for centre of mass only. (You should try to prove it)

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In order to get correct equations you must apply pseudo forces on all the particles on the rigid body (try it!). Then you must find the torque due to the applied pseudo force (I call it 'pseudo-torque').

It is very easy to show (I will leave this an an exercise to you) that the torque due to all the pseudo forces can be obtained by considering the pseudo force acting alone at the Centre of Mass of rigid body.

EDIT: Meaning of accelerating axis: Imagine particles on the rigid

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