Paper 1 Circular Motion Drills

Q1

An angle of one radian subtends an arc length equal to

A. the diameter.
B. the radius.
C. the circumference.
D. $2\pi$ times the radius.

Q2

For circular motion of radius $r$, arc length $s$ and angular displacement $\theta$ in radians are related by

A. $s=r\theta$
B. $s=\theta /r$
C. $s=r/\theta$
D. $s=2\pi r\theta$

Q3

A wheel rotates at $5.0\mathrm{rad}{\mathrm{s}}^{-1}$. Its period is

A. $0.20\mathrm{s}$
B. $0.80\mathrm{s}$
C. $1.26\mathrm{s}$
D. $31.4\mathrm{s}$

Q4

The tangential speed of a point at radius $0.40\mathrm{m}$ rotating at $6.0\mathrm{rad}{\mathrm{s}}^{-1}$ is

A. $0.067\mathrm{m}{\mathrm{s}}^{-1}$
B. $2.4\mathrm{m}{\mathrm{s}}^{-1}$
C. $6.4\mathrm{m}{\mathrm{s}}^{-1}$
D. $15\mathrm{m}{\mathrm{s}}^{-1}$

Q5

In uniform circular motion, acceleration is

A. zero because speed is constant.
B. tangent to the path.
C. directed towards the centre.
D. directed away from the centre.

Q6

Centripetal force is

A. an extra force added to a free-body diagram.
B. the inward resultant of real forces.
C. always tension.
D. always weight.

Q7

Which expression gives centripetal acceleration?

A. $v/r$
B. $r/v^2$
C. $v^2/r$
D. $mr{\omega }^2$

Q8

If speed doubles while radius is unchanged, centripetal acceleration

A. doubles.
B. halves.
C. quadruples.
D. remains unchanged.

Q9

If angular speed doubles while radius is unchanged, centripetal force on the same mass

A. doubles.
B. quadruples.
C. halves.
D. remains unchanged.

Q10

A mass moves in a horizontal circle attached to a string. The real force providing the inward resultant is usually

A. tension.
B. kinetic energy.
C. centripetal force as a separate interaction.
D. velocity.

Q11

A car turns on a flat road at constant speed. The inward force is provided mainly by

A. weight.
B. normal contact force.
C. friction between tyres and road.
D. air pressure only.

Q12

Velocity in uniform circular motion changes because

A. its magnitude changes.
B. its direction changes.
C. acceleration is zero.
D. radius is zero.

Q13

The centripetal acceleration is always

A. parallel to instantaneous velocity.
B. perpendicular to instantaneous velocity.
C. opposite to angular velocity.
D. zero at constant speed.

Q14

A particle completes $20$ revolutions in $5.0\mathrm{s}$. Its frequency is

A. $0.25\mathrm{Hz}$
B. $4.0\mathrm{Hz}$
C. $25\mathrm{Hz}$
D. $100\mathrm{Hz}$

Q15

The angular speed corresponding to frequency $4.0\mathrm{Hz}$ is

A. $4.0\mathrm{rad}{\mathrm{s}}^{-1}$
B. $8.0\mathrm{rad}{\mathrm{s}}^{-1}$
C. $25.1\mathrm{rad}{\mathrm{s}}^{-1}$
D. $39.5\mathrm{rad}{\mathrm{s}}^{-1}$

Q16

For a conical pendulum, the vertical component of tension

A. provides centripetal force.
B. balances weight when vertical acceleration is zero.
C. is zero.
D. equals $m{v}^2/r$.

Q17

For uniform circular motion, the work done by the inward resultant force is zero because

A. force is zero.
B. displacement is zero.
C. force is perpendicular to instantaneous displacement.
D. speed is changing.

Q18

The SI unit of angular velocity is

A. $\mathrm{m}{\mathrm{s}}^{-1}$
B. $\mathrm{rad}{\mathrm{s}}^{-1}$
C. ${\mathrm{s}}^{-2}$
D. $\mathrm{N}\mathrm{k}{\mathrm{g}}^{-1}$

Q19

A student draws an arrow labelled “centripetal force” in addition to tension and weight on a free-body diagram. The main error is that

A. centripetal force should point outward.
B. centripetal force is not a separate real interaction force.
C. weight should point upward.
D. tension cannot provide circular motion.

Q20

The equation $F=mr{\omega }^2$ is equivalent to

A. $F=m{v}^2/r$ if $v=r\omega$.
B. $F=mv/r$.
C. $F=m\omega /r^2$.
D. $F=mvr$.