NCEA Level 3 Physics
Mechanics
This page is designed to test your use of the equations for the
90521 Demonstrate understanding of mechanical systems standard.
Click on the Equation(s), Answer and Unit after each question to reveal the answers.
(There is a pdf of the questions on their own here and with answers here).
The formulae listed in the explanatory notes to the achievement standard will be provided, plus any other required formulae (g = 9.81Nkg^{1}(ms^{2}), G = 6.67 x10^{11}Nm^{2}kg^{2}).
1. A wheel has a radius of 0.3 m. It rotates with an angular velocity of 12 s^{1}. What is the linear velocity of a point on the rim of the wheel?
Equation(s), Answer and Unit
3.6 
ms^{1} 
2. A yoyo, initially at rest, is allowed to fall from a finger. It drops with constant linear acceleration. After 1.40 seconds it has fallen 1.20 m and reached an angular velocity of 4090 revolutions per minute.
What angle (in radians) does the yoyo turn through during the fall of 1.20 m?
Equation(s), Answer and Unit
300 
rad 
3. How much torque is needed to bring a flywheel with moment of inertia 0.2 kg m^{2} rotating at 50 rads^{1}to rest in 20 seconds?
Equation(s), Answer and Unit

0.5 
Nm 
4. A merrygoround is a large, flat, uniform circular disc that can spin around its centre. Its radius is 4.25m and its rotational inertia is 2450 kgm^{2}. The formula for the rotational inertia of a solid disc is: I = ½mr^{2}.
Calculate the mass of the merrygoround.
Equation(s), Answer and Unit
I = ½mr^{2} 
271 
kg 
5. A rotating orbiting satellite has a rotational inertia of the system is 1.20 x 10^{2}kgm^{2}. The satellite is rotating with an angular velocity of 0.100 rads^{1}. Calculate its rotational kinetic energy.
Equation(s), Answer and Unit
0.6 
J 
6. Kelvin stands on the equator of the earth (radius 6.4 x 10 ^{6}m). Find his linear velocity due to the spinning earth.
Equation(s), Answer and Unit

470 
ms^{1} 
7. An electric motor has a rotor with a moment of inertia of 3.9 kgm^{2}. What is the torque required to give it an angular acceleration of 0.40 rads^{2}?
Equation(s), Answer and Unit
1.56 
Kgm^{2}s^{1} 
8. A friction brake acts on a flywheel of moment of inertia 2.0 kg m^{2}and slows it down from an angular velocity of 500 rads^{1}to an angular velocity of 340 rads^{1}in 4.0 s.
What is the torque which the brake exerts on the flywheel?
Equation(s), Answer and Unit

80 
Kgm^{2}s^{1} 
9. A spacecraft is 6.682 x 10^{6}m above the centre of the planet Venus (Mass of Venus = 5.41 x 10^{24}kg, Mass of the spacecraft = 4.32 x10^{4}kg). Calculate the size of the gravitational force acting on the spacecraft.
Equation(s), Answer and Unit
3.49 x 10^{5} 
N 
10. A ballet dancer spins about a vertical axis at 2 revolutions per second with her arms outstretched. With her arms folded her moment of inertia about the vertical axis decreases by 60 %.
Calculate the new rate of revolution.
Equation(s), Answer and Unit
5 
revolutions 
11. A vertical bungee oscillates with an angular frequency of 1.53 rads^{1}. Calculate the period of the simple harmonic motion.
Equation(s), Answer and Unit
4.11 
s 
12. An engineer designs a riding device for an entertainment park. The cages operate at an angular velocity of 2.80 rads^{1}. The rotational inertia of the system is 720 kg m^{2}. Calculate the angular momentum of the cages.
Equation(s), Answer and Unit
2.02 x 10^{3} 
Kgm^{2}s^{1} 
13. A baby bouncer is a springmass system designed to entertain babies before they can walk. The spring constant of the spring is 621 Nm^{1}. The combined mass of the baby and the harness is 9.73 kg.
Calculate the period of the oscillation of the system.
Equation(s), Answer and Unit
0.786 
s 
14. In a car engine the piston moves up and down in the cylinder. The amplitude of the piston is 0.55m and its frequency of oscillation is 140Hz. Calculate the maximum speed of the piston.
Equation(s), Answer and Unit
484 
ms^{1} 
15. A girl at an aquatic amusement park jumps at 2.0 ms^{1}on to a stationary bumper boat. Her mass is mass 48 kg and she lands 0.30 m from the centre. The bumper boat starts spinning at 0.60 rads^{1}.
Calculate the rotational inertia of the bumper boat and the girl combined.
Equation(s), Answer and Unit

48 
Kgm^{2} 
16. A hockey player hits the ball towards the goal. The ball collides with the goalkeeper’s boot at 8.50 ms^{1}. After colliding with the goalkeeper’s boot the ball bounces off her boot at 8.50 ms^{1}again, but at 90.0^{o}to the original direction.
The mass of the ball is 0.175kg. Calculate the change in momentum.
Equation(s), Answer and Unit
2.10 
Kgms^{1} 
17. A boy pushes a ball of mass 225g so it collides with a wall at a right angle. The ball hits at a speed of 0.53 ms^{1} and rebounds at a speed of 0.47 ms^{1}. The collision lasts 0.12s.
Calculate the size and direction of the average force the wall exerts on the ball.
Equation(s), Answer and Unit

1.9 
N 
(Please note: There has been no attempt to show the correct number of significant figures in this exercise)