# Worksheet: Torque

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

**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?

**Q10: **

A pendulum rod of length 1.00 m 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 of with respect to the vertical?

**Q12: **

A man used a wrench to tighten a bolt. He 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 the man 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?

**Q20: **

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?

**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 A?

**Q23: **

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

**Q24: **

A motor is set on a pivoted mount, as shown in the diagram. The weight of the motor is used to maintain tension in the drive belt. When the motor is not running, the tensions and in the drive belt are equal to each other. The total mass of the platform and the motor is 134 kg, and the center of mass of the motor and the platform is at the center of the motor. The diameter of the drive belt pulley is 20 cm.

Find the tension in the drive belt when the motor is **not** running.

Find the force at the hinged platform support at point when the
motor is **not** running.

**Q25: **

To loosen a rusty nut, a 20.0 N force is applied to the wrench handle at angle and at a distance of 0.25 m from the nut, as shown in the diagram.

Find the magnitude of the torque applied to the nut.

Find the magnitude of the torque applied to the nut if .

For what value of is the greatest torque produced?