Physics 12
Centripetal Acceleration Worksheet.
1. A 2 kg stone at the end of a string 0.5 m long is whirled in a horizontal circle. If the magnitude of the
maximum tension that the string can withstand is 36 N, calculate the speed of rotation which would
break the string.
Describe the motion of the 2 kg mass immediately after the string is broken.
(Neglect the effect of air resistance) [3.0 m/s]
2. A 45 kg girl swings on a 2.4 m long light swing with two ropes. At the lowest point in her swing, the
girl’s speed is 5 m/s. Calculate the magnitude of the tension in each rope of the swing when the girl is
at the lowest point of her swing. [4.6 x 102 N toward center]
3. A 0.5 m long rope is used to whirl a 1 kg mass in a vertical circle. When the mass is at the highest
point, its speed was 2.5 m/s. Calculate the magnitude of the tension in the rope when the mass is at the
highest point. [2.7 N toward center]
4. An unknown mass is attached to a light inextensible string which has a length of 3.2 m. The other end of the
string is attached to a fixed point. The mass is made to move in a horizontal circle as shown in the diagram.
When the angle between the string and the vertical axis through the fixed point is 30º, calculate:
a) the instantaneous speed of the mass [3.0 m/s]
b) the frequency of the mass in revolutions per minute. [1.8 x 101 rpm]
5. A child has a mass of 5.0 × 101 kg and swings on a rope 4 m long. What is the tension in the rope if the
child is traveling at 6 m/s as the swings past the lowest point?
[9.4 x 102 N toward center]
6. A bridge over a small river has a roadway which is in the shape of an arch having radius of curvature of
4.1 × 101 m. What is the maximum speed at which an automobile can travel across the bridge without
leaving the bridge? [2.0 x 101 m/s]
7. A motorcycle and rider perform the stunt of circling in a cylindrical track with its axis horizontal. The
diameter of the track is 1.0 × 101 m. The total mass of the rider and the motorcycle is 2.0 × 102 kg.
a) What is the force with which the motorcycle presses against the track at the highest
point if the speed is 12 m/s? [3.8 x 103 N toward center]
b) What is the minimum speed at the highest point if the motorcycle is not to fall from
the track? [7.0 m/s]
8. A car rounds a level curve of radius 65 m at a speed of 18m/s. What is the minimum value of the
coefficient of kinetic friction between the tires and the road to prevent skidding? [0.51]
9. Calculate the banking angle for a curve of radius 150 m such that a car traveling at 25 m/s may make the
turn without depending on friction. [23º]
10. An auto track has semi-circular ends of radius 150 m. The curves are banked at an angle of 52º. At
what speed must the cars be driven to avoid any side-thrust (skidding up/slipping down) on the wheels?
Friction is negligible. [4.3 x 101 m/s]
11. A car having a mass of 1200 kg rounds a curve which is banked at an angle of 18 º to the horizontal.
The radius of the curve is 130 m. Find the speed of the car if the frictional force between the tires and
the road is 3.5 x 103 N down the banked curve.
[2.9 x 101 m/s]
12. A 1500 kg car rounds a curve of radius 75 m at a speed of 25 m/s. The curve is banked at an angle of
22º to the horizontal. Calculate:
(a) the magnitude of the frictional force [6.1 x 103 N toward center]
(b) the coefficient of static friction [3.3 x 10-1]
13. David puts a 0.85 kg rock in his sling and twirls it at 3.0 Hz. The rock moves in a circle with radius
35.0 cm. Ignoring the effect of gravity determine:
(a) the acceleration of the rock [120 m/s2 toward center]
(b) the force that David must exert on the sling [110 N toward center]
(c) the speed of the rock when it is released. [6.6 m/s]
14. A popular amusement park ride is the Gravitron in which riders are enclosed in a cylinder that
spins at 24 rpm. According to Wikipedia the riders experience 4.0 g’s.
(a) Determine the radius at which the riders are positioned. [6.2 m]
(b) Find the speed of the riders. [16 m/s]
15. A small block is placed on top of a rotating horizontal platter at a distance r from the center. The
coefficient of static friction is μs. Derive an expression for the greatest frequency at which the platter
can revolve without the block sliding off.
f 
1
2
g
r
16. A car is traveling on a highway at 20.0 m/s and encounters a curve in the road during which the direction
of the car’s velocity changes by 90.0° in 30.0 s.
(a) Find the car’s centripetal acceleration. [1.05 m/s2]
(b) Derive an expression that gives centripetal acceleration in terms of the three variables in this
problem: v, θ, and t.
a=
 
180 t
17. A mass dangling from the end of a string can be set into motion such that the mass moves in a horizontal
circle as shown in the diagram. The string traces out an imaginary cone; this arrangement is called a
conical pendulum.
(a) Use an analysis of the forces acting on the mass in order to show that the acceleration is given by:
a = g(r/h), where h is the height of the cone.
(b) Derive and simplify an expression for the period of the motion.
T  2
h
g