Paper 1 Circular Motion Answers

Q	Ans	Brief reason
1	B	One radian is defined by $s=r$.
2	A	Radian measure gives $s=r\theta$.
3	C	$T=2\pi /\omega =1.26\mathrm{s}$.
4	B	$v=r\omega =2.4\mathrm{m}{\mathrm{s}}^{-1}$.
5	C	Acceleration is centripetal.
6	B	It is the inward resultant force.
7	C	$a_c=v^2/r=r{\omega }^2$.
8	C	$a_c\propto v^2$.
9	B	$F\propto {\omega }^2$.
10	A	Tension is the real inward force.
11	C	Static friction provides the horizontal inward resultant.
12	B	Velocity is a vector.
13	B	Radial acceleration is perpendicular to tangential velocity.
14	B	$f=20/5.0=4.0\mathrm{Hz}$.
15	C	$\omega =2\pi f=25.1\mathrm{rad}{\mathrm{s}}^{-1}$.
16	B	Horizontal component provides the centripetal resultant.
17	C	Instantaneous force is perpendicular to tangential displacement.
18	B	Angular velocity is measured in radians per second.
19	B	Draw only real forces; centripetal force is their inward resultant.
20	A	Substitute $v=r\omega$ into $m{v}^2/r$.