Slide a ruler parallel to Δv towards the circle. Midway between A and B, Δv points towards the centre of the circle. This is the same direction as the centripetal acceleration
Deriving the equation for the magnitude of the centripetal acceleration
v = r⍵
The acceleration of an object towards the centre of a circle when an object is in motion (rotating) around a circle at a constant speed
Centripetal acceleration is always directed toward the centre of the circle and is perpendicular to the object’s velocity
A domestic washing machine has a spin cycle of 1200 rpm (revolutions per minute) and a diameter of 50 cm.
Calculate the centripetal acceleration experienced by the washing during the spin cycle.
Step 1: List the known quantities
Step 2: Convert the revolutions per minute to revolutions per second
1200 ÷ 60 = 20 rev s−1
Step 3: Convert revolutions per second to angular speed in radians per second
1 rev s–1 = 2π rad s–1
20 rev s–1 = 40π rad s–1 = ω
Step 4: Write the equation linking centripetal acceleration and angular speed
a = rω2
Step 5: Calculate the centripetal acceleration
a = (25 × 10−2) × (40π)2
Step 6: State the final answer
a = 3900 m s−2 (2 s.f.)
A ball tied to a string is rotating in a horizontal circle with a radius of 1.5 m and an angular speed of 3.5 rad s−1.
Calculate its centripetal acceleration if the radius was twice as large and angular speed was twice as fast.
The key takeaways for an object moving in a circle are:
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