In this worksheet, we will practice calculating the torques applied by forces that act at perpendicular distances from axes of rotation.

**Q3: **

The cylindrical head bolts on a car are to be tightened with a torque of 91.0 N⋅m. If a mechanic uses a wrench of length 65 cm, what perpendicular force must he exert on the end of the wrench to tighten a bolt correctly?

**Q4: **

Two flywheels of negligible mass and different radii are bonded together and rotate about a common axis (see the figure). The smaller flywheel of radius 30 cm has a cord that has a pulling force of 50 N on it. What pulling force needs to be applied to the cord connecting the larger flywheel of radius 50 cm such that the combination does not rotate?

**Q5: **

A hanging mass is placed on a cord to keep a pulley from rotating, as shown. The mass on the frictionless plane is 5.0 kg. The inner radius of the pulley is 20 cm and the outer radius is 30 cm. Calculate the mass .

**Q6: **

When tightening a bolt, you push perpendicularly on a wrench with a force of 204 N at a distance of 0.320 m from the centre of the bolt.

How much torque are you exerting relative to the centre of the bolt?

- A 98.3 N⋅m
- B 86.4 N⋅m
- C 63.8 N⋅m
- D 65.3 N⋅m
- E 12.5 N⋅m

**Q7: **

A force of N is applied at the point m. What is the torque of this force about the origin?

**Q8: **

What is the magnitude of the force that must be applied to end of a 5.0-m-long rod laying along the -axis in order to produce a torque on the rod about the origin of N.m?

**Q9: **

A simple pendulum consists of a massless tether 30 cm in length with one end connected to a pivot and a small mass of 2 kg attached to the other end. What is the magnitude of the torque about the pivot when the pendulum makes an angle of with respect to the vertical?

**Q10: **

A pendulum rod that is 1.00-m in length has a mass of 1.00 kg. The upper end of the rod is connected to a pivot and the opposite end of the rod is connected to a solid sphere. The sphere has a mass of 0.500 kg and a radius of 30.0 cm. What is the torque about the pivot when the pendulum is aligned at an angle below the vertical?

**Q11: **

A force is applied at the point , as shown in the diagram. A force acts at point . The object is in equilibrium and has negligible weight.

What is the magnitude of ?

At what counterclockwise angle from the line directed vertically downward from point does act?

**Q12: **

When using a wrench to tighten a bolt, you pushed the wrench with a 176 N force perpendicularly to its length at a point that is 0.180 m away from the center of the bolt measured along the direction of the wrench’s length. What was the magnitude of the torque that you exerted relative to the center of the bolt?

**Q13: **

Two children push normally to opposite sides of a door. One child pushes with a force of 17.5 N at a distance of 0.600 m from the door’s hinges, and the second child pushes at a distance of 0.450 m the hinges. What force must the second child exert to keep the door from moving? Assume friction is negligible.

**Q14: **

A uniform plank of length 8.0 m rests on a level surface with 1.2 m of its length overhanging the end of the surface, as shown in the diagram. The plank has a mass of 40.0 kg. What is the maximum mass that can be supported at the overhanging end of the plank that maintains the equilibrium of the plank?

**Q15: **

Two children push on opposite sides of a door during play. Both push horizontally and perpendicular to the door. One child pushes with a force of 17.5 N at a distance of 0.600 m from the hinges, and the second child pushes at a distance of 0.450 m. What force must the second child exert to keep the door from moving? Assume friction is negligible.

**Q16: **

Wheelbase is the distance between a vehicle’s front and rear axles. A small SUV of mass 1,500 kg has a wheelbase of 3.6 m, and of its weight rests on its front wheels. How far from the front axle is the SUV’s center of mass?

**Q17: **

A flywheel with a radius of 0.50 m is acted upon by the forces , , and , as shown. The magnitude of N, the magnitude of N, and the magnitude of N.

Find the torque produced by .

Find the torque produced by .

Find the torque produced by .

Find the net torque exerted by the forces.

**Q18: **

A mass of 60.0 lb is placed at the end of a 1.00-yard-long horizontal pipe that is pivoted at the end of the pipe opposite to the mass. What is the magnitude of the torque exerted by the mass?

**Q19: **

A gearbox is used to reduce the speed from a motor by a factor of ten. If the input torque to the gearbox is 0.300 kN⋅m and the efficiency of the gearbox is , what is the magnitude of the output torque of the gearbox?

**Q20: **

A force of 5.00 N is applied at the end of a 20.0-centimeter-long wrench. What is the magnitude of the applied torque?

**Q21: **

A 1.00-meter-long narrow dowel of negligible mass is placed at rest in a receptacle, as shown in the accompanying diagram. The dowel is subject to a downward load at the end of the dowel that protrudes from the receptacle. The angle and the distance is 40.0 cm. The force acting at the point A is normal to the axis of the dowel and friction is negligible at this point. What is the magnitude of the net force acting at the end of the dowel from the multiple contact points near the point B?

**Q22: **

A 1.00-meter-long narrow dowel of negligible mass is placed at rest in a receptacle, as shown in the accompanying diagram. The dowel is subject to a downward load at the end of the dowel that protrudes from the receptacle. The angle and the distance is 40.0 cm. The force acting at the point A is normal to the axis of the dowel and friction is negligible at this point. What is the magnitude of the net force acting at the end of the dowel from the multiple contact points near the point B?

**Q23: **

A 1.00-meter-long narrow dowel of negligible mass is placed at rest in a receptacle, as shown in the accompanying diagram. The dowel is subject to a downward load at the end of the dowel that protrudes from the receptacle. The angle and the distance is 40.0 cm. The force acting at the point A is normal to the axis of the dowel and friction is negligible at this point. What is the magnitude of the net force acting at the end of the dowel from the multiple contact points near the point A?

**Q24: **

A large oceangoing ship runs aground near the coastline and lies tilted at an angle as shown in the diagram. Salvage crews must apply a torque to right the ship in order to float the vessel before it can be towed away. The force required to right the ship has a magnitude of N and acts horizontally to the right at a point 100 m away from where the ship contacts the seabed and along a line angled at from the vertical. What torque does the force apply about the ship’s point of contact with the seabed?

- A N⋅m
- B N⋅m
- C N⋅m
- D N⋅m
- E N⋅m