Slide 1
Speed is only part of velocity
Velocity includes direction as well as speed. An object following a curved path accelerates even if its speed remains constant.
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A speedometer does not display direction, so it can stay steady through a bend. Comparing the velocity arrows before and after the bend reveals a change that the speed reading alone conceals.
Slide 2
An inward change
In uniform circular motion, acceleration points toward the circle’s centre. It changes the direction of travel without changing the speed.
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The instantaneous direction of motion lies along a tangent to the circle. Inward acceleration continually bends that tangent; it does not mean the object is steadily approaching the centre.
Slide 3
Tighter turns demand more
At a given speed, a smaller turning radius requires greater acceleration. At a given radius, doubling speed quadruples that acceleration.
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The relation is acceleration equals speed squared divided by radius. At 10 metres per second on a 20-metre-radius circle, the required inward acceleration is 5 metres per second squared.
Slide 4
Name the actual force
Centripetal describes the inward role of a force. It is not an extra force added to tension, gravity or friction.
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For a car turning on a level road, tyre-road friction supplies the inward force. If available friction is insufficient, the car cannot follow the intended curve at that speed.
Slide 5
Release the constraint
If the inward force disappears, the object initially continues along its tangent. It does not need an outward push to leave the circle.
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This follows from inertia: without a net force, the instantaneous velocity persists. Other forces may then bend the subsequent path, so the tangent prediction describes the initial direction rather than every later position.
Sources
- Uniform Circular Motion
OpenStax, Rice University
- Newton’s Laws of Motion
NASA