Describing circular motion: period, angular velocity and v = ωr
Period, frequency, radians and angular velocity, and why a constant speed on a circle still means the velocity is changing.
A ball on a string whirls at a steady speed. Its speed never changes, yet physics says it is accelerating. How can that be?
A wheel completes one revolution in 0.50 s. Its angular velocity is…
A point 0.30 m from the centre of a turntable has ω = 10 rad s⁻¹. Its speed is…
A fan turns at 120 revolutions per minute. Its frequency is…
Two children ride a roundabout, one near the edge and one near the centre. Compared with the child near the centre, the child at the edge has…
A body moves around a circle at a constant speed. Which statement is correct?
A student says: “the satellite is moving at a constant speed so it has no acceleration.” Correct the statement.
Acceleration is the rate of change of…
A body moves in a straight line at constant velocity when…
Key points
- • f = 1 / T and ω = 2π / T = 2πf.
- • v = 2πr / T = ωr; ω is the same for every point on a rotating body, v grows with r.
- • The velocity is tangent to the circle; its direction keeps changing, so the body accelerates.
Formulas
- ω = 2π / T = 2πf
- v = ωr = 2πr / T
Key terms
- Angular velocity ω :
- the angle turned per second, in rad s⁻¹
- Period T :
- the time for one complete revolution
Common errors
- • Using degrees in ω = θ / t
- • Thinking constant speed means zero acceleration
- • Mixing up ω and v